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CALENDARS 



Rules, Explanations, Contradictions 



AS TO 



AC. TO CORRECT THE ERRORS OF NS., OS., AND AM. ; AE.=ACTIAN ; AM.= 

PRESENT GREEK; AU.= ANCIENT ROMAN; HC.=PRESENT HEBREW; 

HCM.=ANCIENT HEBREW; JE.=JULIAN ; ME.— MOHAMMEDAN ; 

NC.=ALEXANDRIAN ; NE.=NABONASSAR; NS.— GREGORIAN ; 

OE.— OLYMPIC ; OS.=OLD STYLE. 



B 



BY 

AYCRIGG 



A.B. AND A.M. OF COL. COLL., NEW YORK; PH.D. OF PENN. COL. ; C. E. 



PRINTED FOR TSE AUTHOR BY 

EDWARD O. JENKINS' SONS 

20 NORTH WILLIAM ST., NEW YORK. 
1886. 



<EC 29 |g£$ 



CALENDARS. 



Rules, Explanations, Contradictions 



AC. TO CORRECT THE ERRORS OF NS., OS., AND AM. ; AE.=ACTIAN ; AM.=- 

PRESENT GREEK; AU.== ANCIENT ROMAN; HC.=PRESENT HEBREW; 

HCM.-=ANCIENT HEBREW; JE.=JULIAN ; ME.=MOHAMMEDAN ; 

NC-=ALEXANDRIAN ; NE.=NABONASSAR; NS.=GREGORIAN ; 

OE.—OLYMPIC ; OS.=OLD STYLE. 



BY 



B. AYCRIGG, 

A.B. AND A.M. OF COL. COLL., NEW YORK ; PH.D. OF PENN. COL. ; C. E. 



V 




PRINTED FOR THE AUTHOR BT 

EDWARD O. JENKINS' SONS, 

20 NORTH WILLIAM ST., NEW YORK. 
1886. 



i^ 



COPYRIGHT, J 886, BY 
B. AYCRIGG. 



THE LIBRARY 

OF CONGRESS 

WAMINOTOM 



PREFACE 



The Appendix will answer the purpose of an explanatory Index. It contains 
explanations of symbols, and contractions, and scientific terms, and general 
principles. And under the head MD., the rales to determine for all time, the 
Mean Dates of new and of full moon, and of the equinoxes and solstices, which 
are proved to be correct by many historic dates, including numerous eclipses. 
And these astronomical rules form the basis of the present examinations. 

The Rules are in all cases so simplified as to be worked by rote, without the 
necessity of understanding the principles which are explained in the notes. And 
no higher mathematics is required than addition, subtraction, multiplication, and 
division by decimals, according to specific directions. 

The Explanations in the notes are condensed by avoiding repetition, and by sub- 
stituting symbols for subordinate rules, and by references to other passages. This 
brings the explanations within a short space for those who assume that the calcula- 
tions are correct and desire only the general result, while the symbols and refer- 
ences will reduce the labor of the student who desires to examine the subjects 
critically, since in some cases the results given by a few figures, require long and 
intricate calculations. 

Contradictions, to what are believed to be correct, are numerous. As far as 
known, these are discussed in the notes, so that the reader has both sides when 
there is a difference. 

Precision is a leading point in this work, and that is frequently overlooked by 
writers on these subjects, as in the following cases : 

First. As to March 21 of the Paschal Canons. The British Act of Parliament 
of 1751 says that in AD. 825— the year of the Council of Nicea — the vernal equinox 
fell "on or about the 21st day of March." All other known authorities assert 
or imply that March 21 was the actual date. Now, the vernal equinox fell 
March 20 in AD. 325, whether counted from midnight at Greenwich, or from 
midnight at Jerusalem, or in Hebrew time, from 6 hours before midnight at Jeru- 
salem. But in all these modes of counting time it fell on March 21 in each third 
year after bissextile about that time, and the Paschal Canon required the latest date 
upon which it could fall, and therefore said : " The 21st day of March shall be 
accounted the vernal equinox." 

Second. As to Turkish dates (ME.). Authors of the highest standing differ as 
to dates. One charges another with error on account of the difference. But 
neither of them defines how he counts his dates. Some dates correspond with 
July 15 and others with July 16 AD. 622 as the beginning of the era. Now : new 
moon fell AD. 622 July 14 at 8 hours 17 minutes AM. at Mecca, and became vis- 
ible before evening after noon of July 15 when the era began. Hence some count 



2 PKEFACR 

the era as beginning July 15 in civil time„ and others as beginning July 16 iD 
Mohammedan time, which like Hebrew time, begins on the previous evening. The 
dates are identical, but require specification. 

Third. As to the ancient Hebrew Calendar (HCM.). All agree that during the 
second temple (which was destroyed by Titus in AD. 70) the beginning of Nisan 
depended upon the actual appearance of new moon. But no known author defines 
at which end of this day of the visible moon did Nisan begin, except Maimonides. 
And he states distinctly that JSTisan began in the evening after the appearance of 
the new moon. And he believes that such was the Mosaic rule. And the facts 
stated by Josephus (who was present) show that the last sacrifices in the temple 
agreed with this rule. Hence by the Mosaic rule Nisan could not possibly begin 
before 18 hours after conjunction, nor could the Passover fall as early as on the 
day of full moon, but might fall two days after the day of full moon. 

Fourth. As to the present Hebrew Calendar (HC). Many different authors 
give different rules, to simplify the calculations in this — the most occult, and the 
most complicated of all calendars. But no known author states distinctly what 
these dates signify when found, except Maimonides, who says : "If the date fall a 
moment before noon, the calendar is celebrated on that day." This gives the rule 
for the present practice. Hence Tisri may commence "a moment" less than 18 
hours before conjunction, and Nisan may commence about 13.V hours before con- 
junction. And this makes the Passovers fell on the day of full moon, or the day 
before full moon. These were impossible under the Mosaic rule which governed 
dates at the time of the Crucifixion, and have an important bearing on the ques- 
tion as to which of the six years, from AD. 28 to AD. 84, assigned by different 
authors, was the actual year of the Crucifixion. 

Fifth. As to the Olympic Era (OE.). No known author professes to give precise 
Olympic dates, except Scaliger. And his rules are only approximations. 

If the reader detect an error he will confer a favor by so informing the author. 

Passaic, N. J. B. AYCRIGG. 

"Nequid actum reputans si quid superessei agendum J* 



AC. 



AC, = AMENDED CALENDAR TO CORRECT THE ERRORS 
OF NS. OS,, AM. 



Sttmmaky, 



The Crucifixion occurred on the 14th day of Nisan, during the second temple, 
when the regular 14th Nisan fell on the day of full moon on, or next after the ver- 
nal equinox, The Quarto-declmans of Asia held Easter on this day, until in AD. 
325, the Council of Nicea decided that it should be held on the Sunday next there- 
after. This date "was annually determined by Egyptian astronomers until the cen- 
tury after the Council, when the Alexandrian Canon (NC.) was adopted as a sub- 
stitute. This gave the correct dates of the 235 new moons in a cycle of 19 years, 
about AD. 325. 

OS. was adopted by the Council of Chalcedon in AD, 534 to give the dates of 
the 19 Paschal full moons in the cycle. It departed from the Nicean rule on three 
points. First, it added only 13 days to the Egyptian dates of new moon, and this 
brought Easter on the forbidden 14th Nisan. Second, it omitted one full moon of 
Nisan, and substituted one full moon of Zif, Third, it assumed that 235 lunations 
are exactly equal to 19 years, which caused an accumulation of moons of Zif. 
And AM. is the same as OS., in a Greek form, and now has five- moons of Zif. 

NS, was established AD. 1582 to correct the errors of OS. And AC. in the 
form of NS., is an astronomical analysis of NC, NS., OS., AM., with the follow 
mg results. 

AC. Table I. illustrates the Egyptian form of the cycle as used in all Christian 
calendars. 

AC. Tables II., III. contain all the corrections of NS. Tables II., III., which 
contain the entire Gregorian system, with the following differences. 

AC. SC. are the same as NS. SC. until AD. 6000. AC, Indexes give the pre- 
cise mean dates of the Paschal full moons in maximum Hebrew time, while NS. 
Indexes are always less, and allow Easter to fall on the forbidden 14th Nisan. 
And after AD. 7789 they will be the 14th Zif in the standard year. And the pres- 
ent Hebrew Calendar has similar departures from the ancient rules. 

In both Tables III. the dates are determined by Egyptian rules. AC. leaves 
them as they fall. But NS, retracts all GN. which fall on April 19 to second 
April 18, and all GN. from. 12 to 19, from April 18 to second April 17. And these 
retractions bring Easter on the forbidden 14th Nisan, when the other dates are cor- 
rect. And they originate in the errors of OS. as above stated. 

Dr. Seabury in his " Theory and Use of the Church Calendar," says : " Science 
must come down from her throne and condescend to accept the cycles which the 
custodians of the Church have treasured up." But the Church itself has frequently 
changed its cycles. It is purely an astronomical question to determine whether 
NS., OS., or AM. represent the decision of the Council of Nicea. Its importance 
is a matter of opinion. Science deals only with facts. 



See NS. Preface. 



AC. 



AC. TABLE I. 



i January. 

j 


February. 


March. 


April. 


May. 


June. 




ft 






ft 






, 








ft 








ft 






ft 




c3 
ft 


c3 
P 
CQ 


£ 

o 


ft 


CQ 


fc 
O 


QQ 

ft 


p 
p 

CQ 


o 

c3 
A 
ft 




to 

1? 

ft 


c3 
PI 

CQ 


& 

o 

c3 
Ph 
ft 




CQ 

Pt, 

e3 

ft 


p 

P 
CO 


& 

& 


00 

>> 

53 

ft 


a 

3 
CQ 


^ 
O 


1 


A 


5 


1 


D 




1 


D 




5 


1 


G 


12 




1 


B 


13 


1 


E 


2 


2 


B 




2 


E 


13 


2 


E 






2 


A 


11 


13 


2 


C 


2 


2 


F 




3 


C 


13 


3 


F 


2 


3 


F 




13 


3 


B 


10 


2 


3 


D 




3 


G 


10 


4 


D 


2 


4 


G 




4 


G 




2 


4 


C 


9 




4 


E 


10 


4 


A 




5 


E 




5 


A 


10 


5 


A 






5 


D 


8 


10 


5 


F 




5 


B 


18 


6 


F 


10 


6 


B 




6 


B 




10 


6 


E 


7 




6 


G 


18 


6 


C 


7 


7 


G 




7 


C 


18 


7 


C 






7 


F 


6 


18 


7 


A 


7 


7 


D 




8 


A 


18 


8 


D 


7 


8 


D 




18 


8 


G 


5 


7 


8 


B 




8 


E 


15 


9 


B 


7 


9 


E 




9 


E 




7 


9 


A 


4 




9 


C 


15 


9 


F 


4 


10 


C 




10 


F 


15 


10 


F 






10 


B 


3 


15 


10 


D 


4 


10 


G 




11 


D 


15 


11 


G 


4 


11 


G 




15 


11 


C 


2 


4 


11 


E 




11 


A 


12 


12 


E 


4 


12 


A 


12 


12 


A 




4 


12 


D 


1 




12 


F 


12 


12 


B 


1 


13 


F 




13 


B 


1 


13 


B 






13 


E 


* 


12 


13 


G 


1 


13 


C 




14 


G 


12 


14 


C 




14 


C 




12 


14 


F 


29 


1 


14 


A 




14 


D 


9 


15 


A 


1 


15 


D 


9 


15 


D 




1 


15 


G 


28 




15 


B 


9 


15 


E 




16 


B 




16 


E 




16 


E 






16 


A 


27 


9 


16 


C 




16 


F 


17 


17 


C 


9 


17 


F 


17 


17 


F 




9 


17 


B 


26 




17 


D 


17 


17 


G 


6 


18 


D 




18 


G 


6 


18 


G 






18 


C 


25 


17 


18 


E 


6 


18 


A 




19 


E 


17 


19 


A 




19 


A 




17 


19 


D 


24 


6 


19 


F 




19 


B 


14 


20 


F 


6 


20 


B 


14 


20 


B 




6 


20 


E 






20 


G 


14 


20 


C 


3 


21 


G 




21 


C 


3 


21 


C 


23 




21 


F 




14 


21 


A 


3 


21 


D 


11 


22 


A 


14 


22 


D 




22 


D 


22 


14 


22 


G 




3 


22 


B 




22 


E 




23 


B 


3 


23 


E 


11 


23 


E 


21 


3 


23 


A 




11 


23 


C 


11 


23 


F 


19 


24 


C 




24 


F 




24 


F 


20 




24 


B 






24 


D 




24 


G 


8 


25 


D 


11 


25 


G 


19 


25 


G 


19 


11 


25 


C 




19 


25 


E 


19 


25 


A 




26 


E 




26 


A 


8 


26 


A 


18 




26 


D 




8 


26 


F 


8 


26 


B 


16 


27 


F 


19 


27 


B 




27 


B 


17 


19 


27 


E 






27 


G 




27 


C 


5 


28 


G 


8 


28 


C 


16 


28 


C 


16 


8 


28 


F 




16 


28 


A 


16 


28 


D 




29 


A 






































30 


B 


16 








30 


E 


14 


16 


30 


A 






30 


C 




30 


F 


2 


31 


C 


5 








31 


F 


13 


5 










31 


D 


13 









AC. Rule 1. For the date and day of the week of all full moons : Add one to the 
year AD., and divide S by the circle 19, and R=GN. Then opposite to GN. in 
AC. Table I, find the date and Sunday letter of each full moon in that year in 
average standard time (from March 1st, AD. 1800, to March 1st, AD. 2100). And 

2 



AC. 



AC. TABLE 1.— Continued. 



July. 


Aug. 


Sept. 


Oct. 


Not. 


Dec. 




i-4 






►4 






A 






A 






a 






a 




03 

a 


& 

d 

GO 




eg 

to 

A 


& 

d 
d 
go 


p 


GO 

A 


d 

3 
GO 


& 

O 


02 

A 


d 

3 
GO 


fc 

o 


A 


d 
d 

GQ 


p 


03 

ft 


d 
d 

GO 




1 


G 




1 


C 


10 


1 


F 


18 


1 


A 


18 


1 


D 




1 


F 




2 


A 


10 


2 


D 




2 


G 


7 


2 


B 


7 


2 


E 


15 


2 


G 


15 


3 


B 




3 


E 


18 


3 


A 




3 


C 




3 


F 


4 


3 


A 


4 


4 


C 


18 


4 


F 


7 


4 


B 


15 


4 


D 


15 


4 


G 




4 


B 




5 


D 


7 


5 


G 




5 


C 


4 


5 


E 


4 


5 


A 


12 


5 


C 


12 


6 


E 




6 


A 


15 


6 


D 




6 


F 




6 


B 


1 


6 


D 


1 


7 


F 


15 


7 


B 


4 


7 


E 


12 


7 


G 


12 


7 


C 




7 


E 




8 


G 


4 


8 


C 




8 


F 


1 


8 


A 


1 


8 


D 


9 


8 


F 


9 


9 


A 




9 


D 


12 


9 


G 




9 


B 




9 


E 




9 


G 




10 


B 


12 


10 


E 


1 


10 


A 


9 


10 


C 


9 


10 


F 


17 


10 


A 


17 


11 


C 


1 


11 


F 




11 


B 




11 


D 




11 


G 


6 


11 


B 


6 


12 


D 




12 


G 


9 


12 


C 


17 


12 


E 


17 


12 


A 




12 


C 




13 


E 


9 


13 


A 




13 


D 


6 


13 


F 


6 


13 


B 


14 


13 


D 


14 


14 


F 




14 


B 


17 


14 


E 




14 


G 




14 


C 


3 


14 


E 


3 


15 


G 


17 


15 


C 


6 


15 


F 


14 


15 


A 


14 


15 


D 




15 


F 


11 


16 


A 


6 


16 


D 




16 


G 


3 


16 


B 


3 


16 


E 


11 


16 


G 




17 


B 




17 


E 


14 


17 


A 




17 


C 


11 


17 


F 




17 


A 


19 


18 


C 


14 


18 


F 


3 


18 


B 


11 


18 


D 




18 


G 


19 


18 


B 


8 


19 


D 


3 


19 


G 


11 


19 


C 




19 


E 


19 


19 


A 


8 


19 


C 




20 


E 




20 


A 




20 


D 


19 


20 


F 


8 


20 


B 




20 


D 


16 


21 


F 


11 


21 


B 


19 


21 


E 


8 


21 


G 




21 


C 


16 


21 


E 


5 


22 


G 




22 


C 


8 


22 


F 




22 


A 


16 


22 


D 


5 


22 


F 




23 


A 


19 


23 


D 




23 


G 


16 


23 


B 


5 


23 


E 




23 


G 


13 


24 


B 


8 


24 


E 


16 


24 


A 


5 


24 


C 




24 


F 


13 


24 


A 


2 


25 


C 




25 


F 


5 


25 


B 




25 


D 


13 


25 


G 


2 


25 


B 




26 


D 


16 


26 


G 




26 


C 


13 


26 


E 


2 


26 


A 




26 


C 


10 


27 


E 


5 


27 


A 


13 


27 


D 


2 


27 


F 




27 


B 


10 


27 


D 




28 


F 




28 


B 


2 


28 


E 




28 


G 


10 


28 


C 




28 


E 


18 


29 


G 


13 


29 







29 


F 


10 


29 


A 




29 


D 


18 


29 


F 


7 


30 


A 


2 


30 


D 


10 


30 


G 




30 


B 


18 


30 


E 


7 


30 


G 




31 


B 




31 


E 


1 








31 


C 


7 








31 


A 


15 


(Notes 17-30, 52, 53.) 





for all time add the Index in AC. Table II, to March 20, and opposite to that 
dale and corresponding Sunday letter and Epact, put GN. 3, and put all the other 
GN. at the same distance from GN. 3, as in AC. Table I. (Notes 17-28.) 

And for the full moons of Nisan, make the dates one day later than in the table, 
and take the date and Sunday letter and Epact of any GN. which falls on or be- 
tween March 21 and April 19, as belonging to that GN. to determine the date of 
Easter. (Notes 17-28.) Or: 

AC. Rule 2. For the dates of the full moons of Nisan : To March 21, add the 
Index of the century in AC. Table II for the standard date of GK 3. And make 

3 



* 



AC. 



AC. TABLE II. 


AC. TABLE IV. 


NS.IY. 






a 
o 

o 

<u 

S-r 
















B 


34 




s 


cs* 

OS 






o 


CO 

0/ 






o 


8 








« 




CO 


S3 


to 


P 






<o 


Q 


u 


M 

CD 








O 




O 


o 


+3 

M 

CO 

to 


<1 

OB 
h 

C3 

CD 


d 


d 


a> 
to 
to 


CO 

i» 
03 


d 


a 
i— i 

d 


© 

03 


o 


03 

•a 
a 



c 


o 

o 

00 




1 


o 

8 

T-H 


s 


>H 


< 




< 


PQ 


N 


< 


< 


e 


23 


GN. 
6 





GN. 
14 


GN. 


325 


25.5867 




5000 


36 


16.9029 


Mar. 21 




1288 


8 


0.9347 




5100 


37 


17.5792 


22 


22 


D 






3 


14 


B 


1600 


10 


1.9234 


B 


5200 


37 


17.2547 


23 


21 


E 


14 






3 




1700 


11 


2.5943 




5300 


38 


17.9305 


24 


20 


F 


3 




11 






1800 


12 


3.2752 




5400 


39 


18.6064 


25 


19 


G 








11 




1900 


13 


3.9510 




5500 


40 


19.2823 


26 


18 


A 


11 




19 




B 


2000 


13 


3.6269 


B 


5600 


40 


18.9582 


27 


17 


B 






8 


19 




2100 


14 


4.3028 




5700 


41 


19.6340 


28 


16 


C 


19 






8 




2200 


15 


4.9786 




5800 


42 


20.3099 


29 


15 


D 


8 




16 






2300 


16 


5.6545 




5900 


43 


20.9878 


30 


14 


E 






5 


16 


B 


2400 


16 


5.3304 


* 


6000 


44 


21.6716 


31 


13 


F 


16 






5 




2500 


17 


6.0062 




6100 


45 


22.3375 


Apr. 1 


12 


G 


5 




13 






2600 


18 


6.6821 




6200 


46 


23.0134 


2 


11 


A 






2 


13 




2700 


19 


7.3580 




6300 


47 


23.6892 


3 


10 


B 


13 






2 


B 


2800 


19 


7.0338 


B 


6400 


47 


23.3649 


4 


9 


C 


2 




10 






2900 


20 


7.7097 




6500 


48 


24.0410 


5 


8 


D 








10 




8000 


21 


8.3856 




6600 


49 


24.7168 


8 


7 


E 


10 




18 






3100 


22 


9.0614 




6700 


50 


25.3927 


7 


6 


F 






7 


18 


B 


3200 


22 


8.7373 


B 


6800 


50 


25.0686 


8 


5 


G 


18 






7 




3300 


23 


9 4132 




6900 


51 


25.7444 


9 


4 


A 


7 




15 






3400 


24 


10.0880 




7000 


52 


26.4203 


10 


3 


B 






4 


15 




3500 


25 


10.7649 




7100 


53 


27.0962 


11 


2 


C 


15 






4 


B 


3600 


25 


10.4408 


B 


7200 


53 


26.7720 


12 


1 


D 


4 




12 






3700 


26 


11.1167 




7300 


54 


27.4479 


13 


30 


E 






1 


12 




3800 


27 


11.7925 




7400 


55 


28.1238 


14 


29 


F 


12 






1 




3900 


28 


12.4684 




7530 


56 


28.7997 


15 


28 


G 


1 




9 




B 


4000 


28 


12.2443 


B 


7600 


56 


28.4755 


16 


27 


A 








9 




4100 


29 


12.8201 




7700 


57 


29.1514 


17 


26 


B 


9 




17 


17 




4200 


30 


13.4980 


•5f 


7789 


58 


0.3323 


18 


25 


C 






6 


6 




4300 


31 


14.1719 


B 


7800 


58 


0.2267 


19 


24 


D 


17 








B 


4400 


3L 


13.8487 




7900 


59 


0.9725 


20 




E 












4500 


32 


14.5236 


B 


8000 


59 


0.6484 


21 




F 












4600 


33 


15.1995 




8100 


60 


1.3243 


22 




G 












4700 


34 


15.8753 




8200 


61 


2.0001 


23 




A 










B 


4800 


34 


15.5512 




8300 


62 


2.6700 


24 




B 












4900 


35 


16.2271 


B 


8400 
8500 


62 
63 


2.3519 
3.0277 


25 
26 


C 
1 D 










(Notes 31-51.) 




(Kule 7. Notes 64, 65.) 


i 



March 21 and April 19 the limits. Then to GN. 3 and to all subsequent GN., 
add 8 in a circle of 19 years. And if this makes GN. 1 to 8, date it one day later, 
but if GN. 9 to 19 date it two days later until the date exceeds the limit, and then 
subtract 30 days to bring it within the limits. (Notes 55, 56.) Or : 

AG. Bule 3. With the same standard date and limits : Subtract 11 days from the 
date of GN. 3 and of all subsequent GN. to find the date of the next larger GN., 
but subtract 12 days from the date of GN. 19 to find the date of GN. 1. And 

4 



AC. 



AC. TABLE III. 





o 
Hi 


jS 


GN. JP.= Golden Numbers used by the Westerns. 








i 


ii 


iii 


iv 


V 


vi 


vii 


viii 


ix 


X 


xi 


xii 


xiii 


xiv 


XV 


xvi 


xvii 
4 


xviii 
15 


xix 

26 


Mar. 21 


C 


23 


8 


19 





11 


22 


3 


14 


25 


6 


17 


28 


9 


20 


1 


12 


23 


" 22 


D 


22 


9 


20 


1 


12 


23 


4 


15 


26 


7 


18 


29 


10 


21 


2 


13 


24 


5 


16 


27 


" 23 


E 


21 


10 


21 


2 


13 


24 


5 


16 


27 


8 


19 





11 


22 


3 


14 


25 


6 


17 


28 


" 24 


F 


20 


11 


22 


3 


14 


25 


6 


17 


28 


9 


20 


1 


12 


23 


4 


15 


26 


7 


18 


29 


" 25 


G 


19 


12 


23 


4 


15 


26 


7 


18 


29 


10 


21 


2 


13 


24 


5 


16 


27 


8 


19 





" 26 


A 


18 


13 


24 


5 


16 


27 


8 


19 





11 


22 


3 


14 


25 


6 


17 


28 


9 


20 


1 


" 27 


B 


17 


14 


25 


6 


17 


28 


9 


20 


1 


12 


23 


4 


15 


28 


7 


18 


29 


10 


21 


2 


" 28 


C 


18 


15 


26 


7 


18 


29 


10 


21 


2 


13 


24 


5 


16 


27 


8 


19 





11 


22 


3 


" 29 


D 


15 


16 


27 


8 


19 





11 


22 


3 


14 


25 


6 


17 


28 


9 


20 


1 


12 


23 


4 


« 30 


E 


14 


17 


28 


9 


20 


1 


12 


23 


4 


15 


26 


7 


18 


29 


10 


21 


2 


13 


24 


5 


" 31 


F 


13 


18 


29 


10 


21 


2 


13 


24 


5 


16 


27 


8 


19 





11 


22 


3 


U 


25 


6 


April 1 


G 


12 


19 





11 


22 


3 


14 


25 


6 


17 


28 


9 


20 


1 


12 


23 


4 


15 


26 


7 


" 2 


A 


11 


20 


1 


12 


23 


4 


15 


26 


7 


18 


29 


10 


21 


2 


13 


24 


5 


16 


27 


8 


" 3 


B 


10 


21 


2 


13 


24 


5 


16 


27 


8 


19 





11 


22 


3 


14 


25 


6 


17 


28 


9 


« 4 


C 


9 


22 


3 


14 


25 


6 


17 


28 


9 


20 


1 


12 


23 


4 


15 


26 


7 


18 


29 


10 


" 5 


I) 


8 


23 


4 


15 


26 


7 


18 


29 


10 


21 


2 


13 


24 


5 


16 


27 


8 


19 





11 


" 6 


E 


7 


24 


5 


16 


27 


8 


19 





11 


22 


3 


14 


25 


6 


17 


28 


9 


20 


1 


12 


" 7 


F 


6 


25 


6 


17 


28 


9 


20 


1 


12 


23 


4 


15 


26 


» 7 


18 


29 


10 


21 


2 


13 


" 8 


G 


5 


26 


7 


18 


29 


10 


21 


2 


13 


24 


5 


16 


27 


8 


19 





11 


22 


3 


14 


" 9 


A 


4 


27 


8 


19 





11 


22 


3 


14 


25 


6 


17 


28 


9 


20 


1 


12 


23 


4 


15 


" 10 


B 


3 


28 


9 


20 


1 


12 


23 


4 


15 


26 


7 


18 


29 


10 


21 


2 


13 


24 


5 


16 


" 11 


C 


2 


29 


10 


21 


2 


13 


24 


5 


16 


27 


8 


19 





11 


22 


3 


14 


25 


6 


17 


" 12 


D 


1 





11 


22 


3 


14 


25 


6 


17 


28 


9 


20 


1 


12 


23 


4 


15 


26 


7 


18 


" 13 


E 





1 


12 


23 


4 


15 


26 


7 


18 


29 


10 


21 


2 


13 


24 


5 


16 


27 


8 


19 


" 14 


F 


29 


2 


13 


24 


5 


16 


27 


8 


19 





11 


22 


3 


14 


25 





17 


28 


9 


20 


" 15 


G 


28 


3 


14 


25 


6 


17 


28 


9 


20 


1 


12 


23 


4 


15 


26 


7 


18 


29 


10 


21 


" 16 


A 


27 


4 


15 


26 


7 


18 


29 


10 


21 


2 


13 


24 


5 


16 


27 


8 


19 





11 


22 


" 17 


B 


26 


5 


16 


27 


8 


19 





11 


22 


3 


14 


25 


6 


17 


28 


9 


20 


1 


12 


23 


" 18 


C 


25 


6 


17 


28 


9 


20 


1 


12 


23 


4 


15 


26 


7 


18 


29 


10 


21 


2 


13 


24 


" 19 


D 


24 


7 


18 


29 


10 


21 


2 


13 


24 


5 


16 


27 


8 


19 





11 


22 


o 


14 


25 




xvii 


xviii 


xix 


» 


ii 


iii 


iv 


V 


vi 


vii 


viii 


ix 


X 


xi 


xii 


xiii 


xiv 


XV 


xvi 




GN. AM. = Golden Numbers used by the Greek Church. 





(Rule 6 ; Notes 29, 30, 61-70, 120-130.) 

when this makes the date earlier than the limit, add 30 days to bring it within the 
limits. (Notes 57, 58.) 

AC. Rule 4. With the same limits : Add the Index of the century to March 24 
or 54 for the key date. Then multiply any GN. by 11, and divide P by 30, and 
subtract R from the key date, and 2d R=the date of that GN., if within the lim- 

5 



^ 



AC. 

Its. If not, then add or subtract 30 days to bring it within the limits. (No tea 
59, 60.) 

AC. Rule 5. Subtract the Index: of the century from 20 or 50 for the key Epact. 
Then multiply any GN. by 11, and add P to the key Epact, and divide S by 30, 
and R=the Epact of that GN. Then by Rule 2, or 3, or 4, find the date of that 
GN. (Notes 61-63.) 

A C. Rule 6. To construct AC. Table III : By AC. Rule 1, or 2, or 3, or 4 and 
AC. Rule 5, find the dates of GN. and their epacts, on and between March 21 and 
April 19, assuming the Index of the century to be O. Then under each GN. JP. 
and opposite to its date and Epact, mark the index o. Then in each column, write 
down the indexes 1 to 29 in consecutive order, counting March 21 as next after 
April 19. Or add 13 days to the dates of the Epacts in the Roman Missal, omitting 
the double Epact (25) special at April 18, and marking Epact 24 at April 19. Then 
at the bottom put the Greek GN. (GN. AM.) 3 more or 16 less than the GN. JP. at 
the top of the column. (Note 64.) 

AG. Rule 7. To construct AC. Table IV : In AC. Table II, find the Index of the 
century. Then in AC. Table III, find the same Index under each GN. JP., and 
over each GN. AM. and opposite to its date and Sunday letter, and Epact. Or, 
find the same in AC. Table I, by AC. Rule 1, for the Full moons of Nisan. 
(Note 65.) 

Contra. Rule 8. For NS. dates and Epacts : Substitute NS. Table II for AC. 
Table II. Then use AC. Rules 1 to 7 with this modification, for NS. Retractions, 
viz. : If any date thus fall on April 19 retract it to April 18, and retract Epact 24 to 
Epact 25. And if any GN. from 12 to 19, thus fall on April 18, then retract it to 
April 17, and retract the Epact from 25 to 26, marking Epact (25) special to be 
used only with GN. 12 to 19. (Notes 66-70.) 

AC. Rule 9. For NS. Dominical for all time, or for AC. Dominical until AD. 
6000: 

Divide the centuries by 4 and twice what does remain 

Take from 6, and to the number you gain 

Add the odd years and their fourth, which dividing by 7 

What is left take from 7 and the letter is given. 

And 1 to 1= A to G. And the letter thus found is for all the days in a common 
year, and for all the days in a leap year after Feb. 29, while the next letter after is 
for all the days before Feb. 29, counting A as next after G. And all the days 
which have the Sunday letter the same as the NS. Dominical for the year, are Sun- 
days dated NS. in that year. And Sunday next after the date of the full moon of 
Nisan is Easter. And the AC. date of the full moon of Nisan is the date of GN. 
by AC. Tables II, III, IV, while the NS. date of the full moon of Nisan is the date 
of GN., by NS. Tables II, III, IV. 

AC. Rule 10. The Sunday Letters for the 1st, 8th, 15th, 22d, 29th of each of the 
12 months in succession, are the initials of the following 12 words : 
At, Dover, Dwells, George, Brown, Esquire. 
Good, Christian, Fitch, And, David, Friar. 

They are given in AC. Table I. They are the same for AC, NS., OS., and for 
all time. 

AC. 1st Example. AD. 1825=GN. 2, which AC. Table IV puts at April 4. Full 
moon in maximum Hebrew time fell AD. 1825 April 4.073,843 and at the begin 

6 



AC. 

ning of the century April 4.1609, and Table shows April 4.14 in AD. 1806. 
But the actual date in Hebrew time was April 8.574. Then NS. Table IV puts 
GIST. 2 on Saturday April 2, and Easter on the actual date of the full moon of 
Nisan April 3d. (Notes 72, 75-80, 89, 91.) 

AC. 2d Example. AD. 1903=GN. 4, which AC. Table IV puts at April 12. The 
actual date of full moon in Hebrew time was AD. 1903 April 12.592,228. And 
this being the third year after leap year, actual time is maximum time. But NS. 
Table IV puts GN. 4 on Saturday April 11, and NS. Easter on the day of the full 
moon of Nisan. (Notes 72, 75-80, 89, 91.) 

AG M Example. AD. 1845 mean full moon fell 3 hours before noon of Sunday 
March 23 at Jerusalem. AD. 1845=GN. 3, which NS. Table IV puts at March 
22, and Easter on the day of full moon March 23. (Notes 73, 75-80.) 

AG. Uh Example. For the Greek Easter. AD. 1864+5508 ; divided by the circle 
19 leaves GN. AM. 19. To which add 3 in a circle of 19=GN. JP. 3, which AC. 
Table IV puts at Thursday March 24, but NS. Table IV puts at Tuesday March 
22. Then full moon fell March 23.317,741. So that if March 23 had been Sun- 
day, Easter would have fallen on the day of full moon if the Greeks had adopted 
NS. By the present Greek rules (AM.) in AD. 1864, the Greek Easter fell April 
19 OS.=May 1st NS., five weeks after the Nicean Easter. And the full moon of 
Zif fell April 21.848,330 NS., as a supernumerary full moon between the Greek 
Easter and the vernal equinox. (Notes 108-119.) 



AC. NOTES. 



CONTENTS. 

Historical basis of AC. as to the Paschal Canons (1). And Mosaic rule (6-8). 
And facts stated by Josephus (9). And present Hebrew Calendar (10). 

Astronomic basis of AC. (12-16). As to March 21 of the Paschal Canons, and 
Contra (14-16). 

AC. Table I. explained (17-28). Contra Alexandrian Cycle NC. GN. (21-26). 
And contains 6936 days-contra 6935 (26). And Epacts of 1874 (29, 30). 

AC. Table II. As to date of Equinox (32-35). And moon later than equinox 
(36-39), contra (40). And AC. SC. (41-46). And AC. Indexes (47), contra (48-51). 

AC. Mules. As to Rule 1 for medium dates (52). And passing into the next 
year (53). And as to Rules 2 to 10 (55-71). 

AC. Examples. 1st, 2d, 3d=Easter on the day of full moon (72, 73). And 4th as 
to Greek Easter in the month Zif (74). 

General Remarks and Contradictions. As to 14th Nisan (75-80). Tables A, B, C 
(81-92). Alexandrian Canon (94-101). Dionysian Cycle errors (102-104). History 
of OS. (105-107). Greek Calendar 108-119). Roman Epacts (120-130). Authors 
of NS. (131). Authors referred to (132). 

HISTORICAL BASIS OF AC. 
Paschal Canons. 

(1). These formed the solar portion of the Alexandrian Canon, which is herein 
termed the Nicean Calendar (NC), and were as follows : " 1st. That the 21st day of 
March shall be accounted the vernal equinox. 2d. That the full moon happening 
upon or next after the 21st day of March shall be taken for the full moon of Nisan. 
3d. That the Lord's day next following shall be Easter day. 4th. But if full 
moon happen upon a Sunday, Easter shall be the Sunday after " (Wheatly, p. 36). 
(1-16, 32, 41-46, 75-80, 94-101). 

(2). These Canons are at present given in the Anglican Prayer Books, thus : 

"Easter day is always the first Sunday after the full moon, which happens 

upon or next after the 21st day of March ; and if full moon happen upon a Sun- 
day, Easter day is the Sunday after." (1.) 

(3). These Canons originated thus : The Evangelists show that the Crucifixion 
occurred on the 14th Nisan. (HC. Notes 77-83.) The " Quartodecimans " of 
Asia held Easter on the 14th day of Nisan, the anniversary of the Crucifixion, 

8 



AC NOTES. 

and upon any day of the week, until in AD. 314 the Council of Aries decided 
against this custom, and in AD. 325 the Council of Nicea confirmed this decision, 
and ordered that Easter should not be held on the 14th day of Nisan, but on the 
Sunday next thereafter (Brady, V. 1, p. 294), ' ' Ne cum Judseis conveniamus " (Missal). 
(1, 77.) 

(4). This was a strictly astronomic date at the time of the Crucifixion, and 
depended upon the actual appearance of new moon. The Egyptians were the 
most skillful astronomers. "The Patriarch of Alexandria was commissioned to 
announce the time of Easter" (Neale, p. 113 ; Seabury, p. 77). " The Fathers of 
the century after the Council of Nicea, ordered the new and full moons to be 
found by the cycle of the moons consisting of 19 years " (Wheatly, pp. 36, 37). 
(6-8, 94-101.) 

(5). This is the Alexandrian Cycle (NC. GN. in JE. Table), of which a part is 
given in Table A. It gives the mean dates of 235 conjunctions in each 19 years 
about AD. 325 in Hebrew time counted from 6 hours before midnight at Jeru- 
salem. This formed the lunar portion of the "Alexandrian Canon." The solar 
portion was the "Paschal Canons," which directed which of these new moons 
should be used as the new moon of Nisan ; from which to determine the date of 
Easter. And about AD. 325, March 21, of the Paschal Canons, was the date of 
the vernal equinox in each third year after bissextile, while the actual date in AD. 
325 was March 20. (1, 14-16, 81-87, 94-101.) 

Mosaic Rule. 

(6). All authors agree, that during the second temple, the beginning of Nisan 
depended upon the actual appearance of new moon. But no known author defines 
at which end of this day, did Nisan begin, except Maimonides, and he and the 
Talmud are the standard Hebrew authorities. 

(7). Maimonides (Col. 236) says : " Each month the moon is occulted and does 
not appear for about two days, more or less, to wit, at the conjunction with the 
sun before the end of the month. Then again it is seen in the evening in the West. 
But in the night in which the moon first appears after its occultation, from that 
the beginning of the month is counted." And (Col. 234) he believes this to be the 
Mosaic rule. (75-80.) 

(8). Now : This states distinctly, that under the rule which prevailed at the 
time of the Crucifixion, " conjunction with the sun (was) before the end of the 
month." And that the month did not begin until after the appearance of the new 
moon. Newton and Smyth say, that the moon has never been seen earlier than 
18 hours after conjunction. Consequently Nisan could not begin earlier than 18 
hours after conjunction. And full moon is 14 days 18 hours after conjunction. 
Consequently the 14th day of Nisan was the day of full moon, and full moon could 
not possibly fall later than the end of the 14th Nisan. And the full moon of 
Nisan was the full moon which fell on, or next, after the vernal equinox. And 
about AD. 325 the 21st March was the latest date of the equinox. Hence the 
Paschal Canons, by forbidding Easter to be held on the day of full moon on or 
next after March 21 represented the Nicean rule, that Easter must not be held on 
the 14th Nisan. (1, 14-16, 72, 73, 75-80.) 

(9). A 1c o : Josephus was in Jerusalem in AD. 70, at the time of the destruction 
of the second temple. As a contemporary historian he describes what then occurred. 

9 



' 



AC. NOTES. 

In his Antiquities, Book 2, Chap. 4, Sec. 6, and B. 3, C. 10, S. 5, and B. 11, C. 4, 
S. 8, and Wars, B. 5, C. 3, S. 1, he shows that what Moses directs to be done on 
the 14th day of the First Month (Ex. xii. 3-6) was done on the 14th Xanthicus, 
which Scaliger says was the Macedonian name for the Roman month April. And 
mean full moon fell at Jerusalem AD. 70, at 3 hours 37 minutes before noon of 
April 14. This historic fact, proves that the day of full moon was the 14th Nisan 
at the last sacrifices in the temple, and this agrees with the Mosaic rule stated by 
Maimonides. (7, 10, 11, 75-80.) (HC. Note 76, 178.) 

(1C). Also : The lunar dates by the present Hebrew Calendar, are so wonder- 
fully accurate that they are assumed to be perfect, when used to prove the neces- 
sity of modifying the present rules to determine ancient dates (HCM.). Its author, 
and the time of its construction, are unknown. Its solar and lunar dates indicate 
that it is based on astronomic facts in AD. 607, when it agrees almost precisely 
with the Mosaic rule if properly interpreted. The author doubtless applied his 
rules to this most important date, when the last sacrifices were offered in the tem- 
ple and the Hebrews ceased to be a nation. Then if the Hebrew day be counted 
by the Mosaic rule as beginning in the evening after conjunction, it makes the 14th 
day of Nisan fall on the day of full moon April 14, AD. 70. (9, 75-80.) (HC. 
Notes 22-26.) 

(11). Hence, the Paschal Canons and their history, and the Mosaic rule, and the 
historic fact as to the last sacrifices in the temple, and the present Hebrew calendar, 
when interpreted in accordance with the ancient rule, all concur in proving that 
the date of the full moon of Nisan is the forbidden 14th Nisan. (1, 7-10, 75-80.) 

Astronomic Basis of AC. 

(12). MDT. and MDB. (Appendix) are in precise accordance with a mean year 
of 305.242,216 days, and a mean lunation of 29.580,589 days. And these are proved 
to be correct by many historic dates, including the earliest recorded solar date 2,800 
years before AD. 1869 (MD. 4th Ex.), and the earliest recorded lunar date 2,600 
years before AD. 1880 (MD. 2d Ex.) (35). The mean year of 365.242,216 is the es- 
timate in GNA. since 1857. Previously it was Bessel's estimate 865.242,217. De- 
lambre gives 365.242,256 ; Biot, 365.242,245. Brady (p. 50) says that Newton's es- 
timate was 365.242,326, and that Dr. Kelly, who made some improvements in 
GNA., gives 865.242,222 ; Jarvis (p. 103) uses 365.242,234 ; Delambre (Vol. 1, p. 8) 
says that the authors of NS. thought that 365.242,546,2 was near enough for several 
centuries. They do subtract 0.0075 from the Julian year of 365.25, and that makes 
365.242,500. (83-35.) 

(IS). Then, by MDT., find the minimum standard date of the equinox, or of the 
moon, and add JCC. for calendar date. Then verify the calculation by finding the 
same date precisely by MDB. Then to minimum standard date add 1.098,148 for 
maximum Hebrew date. That is, add 0.098,148 for longitude of Jerusalem, 2 
hours. .21 m. .20 sec. east of Greenwich ; +0.25 to count in Hebrew time from 6 
hours before midnight ; +0.75 for maximum time, or actual time in the third year 
after bissextile. Thus : 

(14). In AD. 325 the vernal equinox fell March 20.332,586 in minimum standard 
time. Add 0.25 JCC.=March 20.582,586 actual standard time as found by MDB. 
Then to March 20.332,586 add 1.098, 148= March 21.430,734 in maximum Hebrew 
time, or actual Hebrew time in each third year after bissextile about AD. 325, when 

10 



AC. NOTES. 

the recession of 0.007,784 day per year is excluded. But the actual time in AD. 
325 was March 20.680,734, when counted from midnight at Jerusalem, or March 
20.930,734, if counted from 6 hours before midnight at Jerusalem. (15, 16, 
31-35, 83.) 

(15). Contra. All the following assert or imply that the actual date of the ver- 
nal equinox in AD. 325 was March 21, without stating in what kind of time, viz. : 
Long (1255) says : "The equinox in common years near AD. 325 was March 21." 
And Montucla (Vol. 1, p. 582) says : "At the time of the Council of Nicea, the 
vernal equinox fell March 21." And Renwick (Vol. 2, p. 201) says : " The Coun- 
cil of Nice, in the year AD. 325, finding the equinox on March 21." And liees 
(Calendar) says : " Sosigenes, in the reign of Julius Csesar, had observed the vernal 
equinox on March 25. At the Council of Nice it was fixed at March 21. In 1582 
it was brought back to March 21." And Adams (Roman year) says : "Equinox 
fell AD. 325, March 21." And the Missal (De festibus mobilibus) says : " [Since, 
according t« the decree of the Nicean Council, Easter must be celebrated on Sun- 
day next after the 14th day of the first month, to wit, that w T hich among the He- 
brews is called the first month, of which the 14th of the moon falls on or next after 
the vernal equinox, which falls on the 21st of March." And to the same effect, 
see Wheatly (pp. 35-38), and Seabury (pp. 105, 110, US). But Scabury (p. 190) 
quotes the Act of . Parliament of 1751, as "On or about the 21st day of March." 
And Wheatly (p. 37) says: "For want of better skill in astronomy, the Paschal 
Canons confined the equinox to March 21." (1, 14, 31-35.) 

(16). Now. The "skill in astronomy "is proved by giving the canon, "That 
the 21st day of March shall be accounted the vernal equinox." Had March 20, the 
actual date in AD. 325, been given, then would Easter have fallen on the forbidden 
14th Nisan in each third year after bissextile, when full moon fell on Sunday, 
March 21. (1, 14, 31-35.) 

CONSTRUCTION OF AC. TABLES I. AND II. 
AC. Table I. 

(17). Count Jan. 54 and 83 (Feb. 23 and March 24) as the limits of the first 
month of the lunar year, and GN. 11, Jan. 54 the first GN. in the year. Then to 
Jan. 54 continue to add, alternately, 30 and 29 days in a circle of 335 day, until the 
date falls within the limits. Then and in all cases begin the first month with 30 
days and continue the alternation 30 and 29 until the date falls within the limits. 
And at each addition mark the same GN. until the date exceeds Jan. 385, and then 
add one year to the GN. when 365 is subtracted from the date — except, make the 
year GN. 19 386 days, and when the date exceeds Jan. 386, then subtract 366 to 
find the date of GN. 1. (25, 26.) 

(1§). This extends through the whole cycle, the Egyptian rules, as shown in 
Table A from GN. 16, Feb. 6, to GN. 5, April 7. AC. Rule 2 shows that the 
small GN. from 1 to 8 fall half a day too early, and the large GN. from 9 to 19 fall 
half a day too late for the average. Hence, when a small GN. begins the series, 
the last of the series will fall on the 30th day. But when a large GN. begins the 
series, the last of the series will fall on the 28th day. Hence, the large GN. 11 is made 
the first GN. of the first month of the lunar year at Jan. 54, so that in the alterna- 
tion the short months of 29 days may contain the whole series. (55, 66-70, 81.) 

11 



AC. NOTES. 

(19). Also : The alternation of 30 and 29 days interrupts the regular succession 
of dates at each junction where the long months begin, as shown by a large GN. 
following one day after a small GN., as at April 23, June 21, Aug. 19, Oct. 17, 
Dec. 15. Also at Feb. 12 when GN. 12 is only one day later than GN. 4. But 
these are in the same lunar years as the previous GN. 11 and 3, which have one 
year additional to make them count in Julian years. (66-70, 81.) 

(20). Now. The standard is GN. 3, and as the Index in AC. Table II. advances 
from to 29, GN. 3 will advance from March 21 to April 19. And when GN. 3 
falls on March 21, the irregularity at the junction will fall at GN. 11 April 21. 
And as GN. 3 advances to April 19, this junction will at the same time be carried 
forward, and at the same time the previous junction, which now stands at GN. 12, 
Feb. 12, will be carried forward to March 11. Hence, in no case during the Great 
Lunar cycle of 6501 years will the regularity of the dates of the 19 full moons of 
Nisan, on or between March 21 and April 19, be interrupted by the junction of the 
long with the short months. (66-70.) 

(21). Contra. In the Egyptian cycle (81) the junction falls at GN. 16, April 6, and 
the addition of 13 days if continued would have brought this junction to GN. 16, 
April 19. This junction of GN. 16, April 6 happened to fall at this date because this 
Egyptian cycle pays no regard to the solar dates of the new moons of Nisan. But 
AC. Table I. is prepared for Hebrew dates, and when a small GN. falls on March 
21 , or a large GN. falls on March 22, then the regular date of the last of the series 
falls on April 19. And AC. leaves them at the regular dates. But Contra, Rule 8 
retracts all GN. which regularly fall on April 19 to April 18. And if this be a 
small GN. from 1 to 8, it regularly falls only one day after the large GN. from 12 
to 19. Then, to prevent two GN. falling on the same day, the large GN. from 12 
to 19 is retracted from April 18 to April 17. And these retractions are produced in 
the Roman mode by increasing the epacts as shown in Table A (81), and in the 
Anglican mode, by retracting the dates in NS. Table III. (66-70.) 

(22). Also, as to AC. Table I. All cycles of 19 years necessarily have 12 com- 
mon years of 12 months and 7 Embolismic years of 13 months. Two of such cycles 
are strictly astronomic. MDT. counts 235 mean lunations of 29.530,589 days. The 
present Hebrew Calendar (HC.) counts 235 lunations of 29 days.. 12 hours 793 
scruples, of which 1080=one hour, and this lunation is less than half a second 
longer than 29.530,589 days. The Metonic Cycle (OE.) counts nothing less than 
whole days, but it counts every day as one. The Egyptian Cycle counts nothing 
less than whole days and makes no difference for the extra day in a leap year. But, 
while the Hebrew Calendar is the most occult and the most complicated of all cal- 
endars, the Egyptian rules are the most simple. 

(23). The Egyptian cycle is counted in years of 365 days. And 19 years of 365 
days=3935 days. Then 235 months alternately 30 and 29 days would count 6933 
days. AC. Table I. always begins the year with a month of 30 days, so that the 7 
embolismic months have 30 days each. Then the cycle contains 228 months alter- 
nately 30 and 29 days, and 7 embolismic months of 30 days =3936 days. Then at 
the end of the cycle, AC, Table I. adds one intercalary day to the 19 years of 365 
days to make the days in the years 3936, the same as the days in the months. Then 
when these years of 365 days are expanded to 365.25 by being counted in Julian 
time, the average length of the month is almost precisely the length of a mean lu 
nation. 

12 



AC. NOTES. 

(24). In AC. Table I. each of these 7 embolismic months of 30 days, ends, and 
a second month of 30 days begins, at each of the first 7 GN. of the series, from Feb. 
23 to March 4, viz., at the beginning of GN. 11, 19, 8, 16, 5, 13, 2. So that there is 
a regu.ar succession of dates by AC. Kules 2 to 4 from Feb. 12 to April 22, and 
thereafter from GN. 11, for two months in succession throughout the cycle, with- 
out the irregularities at the junctions. 

(25). Contra. In the Alexandrian Cycle (81) the same rules apply to the part 
from Feb. 6 to April 5. But not to the whole of the cycle (JE. Table). The 7 ex- 
tra months of 30 days begin at these dates : GN. 3, Jan. 1, GN. 5, Sept. 2 ; GN. 8, 
March 6, GK 11, Jan. 3, GK 13, Dec. 31, GK 16, Sept. 1 ; GN. 19, March 5. 
But the greatest difference is in the year GIST. 19 in which the dates of the months 
run thus: Jan. 5 ;+29=34 ;+30=64 ;+30 again=94 ;+29=123 ;+30=153 ;+29= 
182;+29again=211 ;+29 for the third time =240 ;+30=270+29=299 :+30=329 ;+ 
29=358 ;+30=388. Then subtract 365 leaves Jan. 23 for GN. 1. 

(26). This makes it appear as if the 235 months are contained in 19 years of 365 
days without the intercalary of AC. Table I. But this intercalary is contained in 
this irregular alternation. This is proved by AC. Rules 3, 4, 5, in which the inter- 
calary must be included to find the dates in the Alexandrian cycle, on and between 
Feb. 6 and April 5, with either of the GN. and its date, used as the standard. (53, 
55-65.) 

(27). AC. Table I. puts GN. 3 at March 23 or two days after March 21. This 
would be for Index 2, and for ecclesiastical dates all the GN. must be taken one 
day later than in the table to agree with AC. Index 3 from the beginning of this 
century to March 1st AD. 2100, so that in all cases the latest possible date in He- 
brew time shall be given. 

(2§). But AC. Table I., for average standard dates sometimes makes the dates 
too late and sometimes too early for the actual dates. Thus : take the four years 
near the middle of this century (of which the Nautical Almanacs are at hand) and 
in AD. 1855 the average actual full moon fell at 11 hours after the beginning of 
the table date. In 1856 at 9 hours before the beginning of the table date. In 1857 
at 7 hours before. In 1858 at 2 hours after.. The average of the four years is three 
hours before the beginning of the table date. MDE. Table (A) gives the precise 
mean date during the present cycle. This can be compared with AC. Table I. 
(MDE. 3d Ex.) 

(29). As to the Epacts in AC. Table I. The Missal gives the following : "Table 
of Epacts corresponding with the Golden Numbers, from the Ides of October in 
the year of correction 1582 (first subtracting ten days) to the year 1700 exclusive." 



GN 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


1 


2 


3 


4 


5 


Epacts. . . 


26 


7 


18 


21 


10 


21 


2 


13 


24 


5 


16 


27 


8 


19 


1 


12 


23 


4 


15 


And a 


second table from 1700 to 1900 exclusive, thus : 










GN. 


10 


11 


12 


13 J 14 


15 


16 


17 18 


19 


1 


2 


3 


4 


5 


6 


7 


8 


9 


Epacts 


9 


20 


1 


12 23 


4 


15 


26 | 7 


18 


* 


11 


22 


3 


14 


25 


6 


17 


28 



13 



AC. NOTES. 

Now : Index 0, puts all the GN. two days earlier than in AC. Table I., and 
brings them opposite to the same Epacts as the first table in the Missal. And 
Index 1 puts all the GN. one day earlier than in AC. Table I., and brings them oppo- 
site to the same Epacts as in the second table in the Missal. As the GN. now stand 
in AC. Table 1, they represent the second change corresponding with Index 2. 
And thus as GN. 3, advances from March 21 to April 19, the 30 changes of Epacts 
will be given to find ecclesiastical dates in the Roman mode, by NS. Table VII. — 
except that AC. obliterates the NS. Retractions. 

(30;. In a part of this work which was printed in 1874, a column of Epacts 
was added to NS. Table III., with these remarks : " Table III. is the Anglican Table 
III, with the addition of the column of Epacts, to be used with Table VII. These 
are found, by adding 13 days to the dates of the same Epacts for the Paschal New 
Moons in the Missal. This column, with the assistance of the Anglican Tables II. 
and III., will for all time show the 30 changes of Epacts during each Great Cycle. 
The Missal gives two tables and 52 lines of printing for the single change of Epacts 
from AD. 1582 to 1899, and says : • De qua re plura invenies in libro novce rationis 
restituendi Kalendarii Romani,' but does not give the name of the 'book.' De- 
lambre (Vol. 1, p. 18) says that Clavius gives 217 combinations. Long (1266-8) 
gives three tables here represented by Indexes 0, 1, 2 ; and says that Clavius gives 
30 series of Epacts, and tables up to AD. 303, 300. See Jarvis (p. 107) ; Wheatly 
(pp. 37-47) ; Seabury (p. 201) ; Rees (Cycle, Number)." (61-63, 120-130.) 



U 



(31.) 



AC. NOTES. 



AC. TABLE II.— Construction. 













<* a 












d 00 . 








b 

a 

.: "a 


co m 


o(J5 








j- 

a 

.5 a 


co M 
. o 

£.2 


cdOS 


co 

1 


<! 

CO 


d 

C/2 


nil Equinox 
. Hebrew, 
OS. 
7784 per ce 


Moon of G 
3 after Equ 
454,268,42 
r century. 


Indexes, 
ar. 21 AC— 
Full Moon 
Max. Hebr 


V 

M 

CD 




d 

02 


ial Equinoj 
. Hebrew, 
OS. 

7784 per ce 


Moon of G 
3 after Equ 
454,268,42 
r century. 


Indexes. 
arch 21 = 
Full Moon 
ax. Hebrew 


CO 

on 




d 


8 * « | 


3 >>© ? 
a <a ~ 


d^c.S 


CO 

CO 


03 
CD 


d 


§«§?" 


?&* 


d^c£ 


s 


H 


< 


t>£4 1 


P^« + 


<5 + 


s 


H 


<j 


>%£ 1 


feQ + 


< + 




325 





80.4307 


25.1560 


25.5867 


5000 


36 


44.0405 


16.8624 


16.9029 




12S8 


8 


72.9347 


0.0000 


0.9347 




5100 


37 


43.2621 


17.3167 


17.5792 


B 


1600 


10 


70.5061 


1.4173 


1.9234 


B 


5200 


37 


42.4837 


17.7710 


17.2547 




1700 


11 


69.7227 


1.8716 


2.5943 




5300 


38 


41.7053 


18.2252 


17.9305 




1800 


12 


68.9493 


2.3259 


3.2752 




5400 


39 


40.9269 


18.6795 


18.6064 




1900 


13 


68.1709 


2.7801 


3.9510 




5500 


40 


40.1485 


19.1338 


19.2823 


B 


2000 


13 


67.3925 


3.2344 


3.6269 


B 


5600 


40 


39.3701 


19.5881 


18.9582 




2100 


14 


66.6141 


3.6887 


4.3028 




5700 


41 


38.5917 


20.0423 


19.6340 




2200 


15 


65.8357 


4.1429 


4.9786 




5800 


42 


37.8133 


20.4966 


20.3099 




2300 


16 


65.0573 


4.5972 


5.6545 




5900 


43 


37.0349 


20.9509 


20.9878 


B 


2400 


16 


64.2789 


5.0515 


5.3304 


* 


6000 


44 


36.2565 


21.4151 


21.6716 




2500 


17 


63.5005 


5.5057 


6.0062 




6100 


45 


35.4781 


21.8594 


22.3375 




2600 


18 


62.7221 


5.9600 


6.6821 




6200 


46 


34.6997 


22.3137 


23.0134 




2700 


19 


61.9437 


6.4143 


7.3580 




6300 


47 


33.9213 


22.76'J9 


23.6892 


B 


2800 


19 


61.1653 


6.8685 


7.0338 


B 


6400 


47 


33.1429 


23.2222 


23.3649 




2900 


20 


60.3869 


7.3228 


7.7097 




T.500 


48 


32.3645 


23.6765 


24.0410 




3000 


21 


59.6085 


7.7771 


8.3856 




6600 


49 


31.5861 


24.1307 


24.7168 




3100 


22 


58.8301 


8.2313 


9.0614 




6700 


50 


30.8077 


24.5850 


25.3927 


B 


3200 


22 


58.0517 


8.6856 


8.7873 


B 


6800 


50 


30.0293 


25.0393 


25.0686 




3300 


23 


57.2733 


9.1399 


9.4132 




6900 


51 


29.2509 


25.4935 


25.7444 




3400 


24 


56.4949 


9.5941 


10.0890 




7000 


52 


28.4725 


25.9478 


26.4203 




3500 


25 


55.7165 


10.0484 


10.7649 




7100 


53 


27.6941 


26.4021 


27.0962 


B 


3600 


25 


54.9381 


10.5027 


10.4408 


B 


7200 


53 


26.9157 


26.8563 


26.7720 




3700 


26 


54.1597 


10.9570 


11.1167 




7300 


54 


26.1373 


27.3106 


27.4479 




3800 


27 


53.3813 


11.4112 


11.7925 




7400 


55 


25.3589 


27 7649 


28.1238 




3900 


28 


52.6029 


11.8655 


12.4684 




7500 


56 


24.5805 


28.2192 


28.7997 


B 


4000 


28 


51.9245 


12.3198 


12.2443 


B 


7600 


56 


23.8021 


28.6734 


28. 47 '.5 




4100 


29 


51.0461 


12.7740 


12.8201 




7700 


57 


23.0237 


29.1277 


29.1514 




4200 


30 


50.2677 


13.2283 


13.4i;60 


* 


7789 


58 


22.3309 


0.0014 


0.3323 




4300 


31 


49.4893 


13.6826 


14.1719 


B 


7800 


58 


22.2453 


0.0514 


0.2967 


B 


4400 


31 


48.7109 


14.1363 


13.8477 




7900 


59 


21.4669 


0.5056 


0.9725 




4500 


32 


47.9325 


14.5911 


14.5236 


B 


8000 


59 


20.6885 


0.9599 


0.6484 




4600 


33 


47.1541 


15.0454 


15.1995 




8100 


60 


19.9101 


1.4142 


1.3243 




4700 


34 


4:1.3757 


15.4996 


15.8753 




8200. 


61 


19.1317 


1.8684 


2.0001 


B 


4800 


34 


45.5973 


15.9539 


15.5512 




8300 


62 


18.3533 


2.3227 


2.6760 




49U0 


35 


44.8189 


16.4082 


16.2271 


B 


8400 
8500 


62 
63 


17.5749 
16.7965 


2.7770 
3.2312 


2.3519 
3.0277 



AC. Table II. Explained. 
(32). As to the date of the equinox (31). The vernal equinox fell AD. 325 Jan. 
79.332,586, and AD. 1600, Jan. 69.407,986 in minimum standard time. Then add 
1.098,148 makes AD. 325 Jan. 80.430,734, and AD. 1600 Jan. 70.506,134 in maxi- 
mum Hebrew time. Then continue to subtract 0.7784 day per century for the dates 
of the equinox in the centurial years, for the difference between 100 Julian years 
of 365.25 days and 100 equinoxial years of 365.242,216 days. (12-16, 33-35.) 

15 



AC. NOTES. 

(33). NS. SC. subtracts 0.75 day from 100 Julian years, and this makes the 
NS. year =365. 242, 500, or a difference of one day in 3521 years. (12, 35.) 

(34). Contra. Delambre says that the error is one day in 3600 years. Thia 
makes the equinoxial year 365.242,222 days. (12, 33, 35.) 

(35). Now. The Greenwich Nautical Almanac assumed 365.242,217 up to 1856, 
when (p. 581) it says : " The equinoxial year has been assumed, according to Bessel 
{Conn, des Temps, 1831, Additions, p. 154), equal to 365.242,217 mean solar days." 
But in 1857 the estimate was changed to 365.242,216 days. And this agrees with 
the earliest solar date on record, 2300 years before 1869 (MD. 4th Ex.). (12.) 

(36). As to moon later than equinox in AC. Table II. (31). 19 equinoxial years 
of 365.242,216 days= 6939. 602, 104 days. And 235 lunations of 29.530,589 days 
=6939.688,415 days. The difference 0.086,311 divided by 19 years gives 
0.004,542,684,2 day per year, that the moon represented by any GN., advances in 
equinoxial date. And this into 29.530,589 gives 6500.692 years for it to advance a 
full lunation after the vernal equinox, and to become the full moon of Zif , when 
the full moon one lunation earlier becomes the full moon of Nisan. (39, 40.) 

(3r>. The standard is the full moon of GN. 3. And AD. 1883 =GN. 3 when 
the full moon fell 2.702,894 days after the vernal equinox. This divided by the 
rate per 3^ear=595 years. And this from AD. 1883 leaves AD. 1288 when the 
moon coincided with the equinox. Then for the fractions. In AD. 1275 =GN. 3 
the moon fell 0.059,058 before the equinox. In 13 years it advanced in equinoxial 
date 0.059,055. Hence AD. 1288 the full moon of GN. 3 at its regular advance and 
assuming that this was its year, fell 0.000,003 before the equinox. (101.) (HC. 65.) 

(3§). Also AD. 1598=GN. 3, full moon fell 1.408,229 after the equinox. Add 
0.009,085 its advance for two years=l. 417,314 day after the equinox in AD. 1600. 
To this continue to add 0.454,268,42 for the advance per century. (32, 36.) 

(39). The next great cycle will begin 6500.692 years after AD. 1288= AD. 7789. 
AD. 7773= GN. 3, when full moon falls 29.459,304 after the equinox. Add the 
advance for 16 years, makes 29.531,987 that the present moon will fall later than 
the equinox in AD. 7789. Subtract a lunation, leaves 0.001398, that the next full 
moon of Nisan in GN. 3 will be later than the equinox in AD. 7789. Hence AD. 
7789 will be the beginning of the next Great Lunar Cycle. Then add 11 years 
advance makes the next standard moon of Nisan fall 0.051,367 after the equinox 
in AD. 7800. Then as before continue to add 0.454,268,42 per century. (32, 36.) 

(40). Contra. NS. Table II. makes the next Great Lunar Cycle begin in AD. 
8500, when AC. Table II. makes the next moon fall 3.2312 days after the equinox. 
And this is in absolute time, independent of artificial time. (31.) 

As to AC. SC. m AC. Table II. 

(41). As in the Julian Calendar (OS.), count every year AD. as a bissextile 
which leaves no remainder when divided by 4, except the centurial years. And 
then omit the intercalaries in every centurial year, of which the centuries leave a 
remainder when divided by 4, with these exceptions. Omit the intercalary in AD. 
6000 and in AD. 7788, and insert it in AD. 7800. Then, beginning with 10 days 
AC. SC. in AD. 1600, add one day for each intercalary OS. that is omitted. 

(42). This makes AC. SC. the same as NS. SC. until AD. 6000, and thereafter 
one day more, and removes the NS. intercalary from AD. 7788 to AD. 7800. And 
for these reasons. (71.) 

16 



AC. NOTES. 

(43). To make the date of the vernal equinox fall invariably on March 21 of the 
Paschal Canons in the centurial year, subtract the whole number of its date OS. 
from Jan. 80. Thus, in AD. 1600, Jan. 70 from Jan. 80=10 AC. SC, and the 
equinox falls March 21. 5061, AC. But before the end of the century it will fall 
on March 20, because with every fourth year as a bissextile its date recedes 0.7784 
per century. And hence, if the actual date be not later than March 21 in the be- 
ginning of the century, it cannot become so during the century. (1, 32-36.) 

(44). Again. "With the present system of omitting three intercalaries in four 
centuries, it is not practicable to make the equinox always fall on March 21 at the 
beginning of the century. When AC. SC, added to the date OS. of the equinox 
makes Jan. 79, it falls on March 20, as in 4000, 4400, 4800, 4900, 5200, 5300, 5400, 
5600, 5700, 5800. And it would do so in AD. 6000, if the intercalary of NS. were 
retained. Before 6000 there can be no omission of the NS. intercalary without occa- 
sionally making the equinox fall on March 22, and thus bringing Easter on the for- 
bidden 14th Nisan. But by retaining the intercalary in 6000, the date would then 
and thereafter vibrate between March 19 and March 20, and never fall as late as 
March 21 . This would never bring Easter on the forbidden 14th Nisan, but it 
would cause unnecessary postponements. 

(45). Then the departures from the system, by omitting the intercalary at AD. 
7788, is necessary to make the date March 21 on the beginning of the next great 
lunar cycle, so that the Index may be zero. Then it is inserted irregularly in AD. 
7800, to prevent the date thereafter exceeding March 21. 

(46). There is a defect in AD. 1900, when the actual date of the equinox will be 
March 22. 1709, AC. or NS. But in 22 years the date will recede to March 21. 

As to the Indexes m AC. Table II. (31). 

(47). Add together the day of Jan. OS. of the date of the vernal equinox and 
fraction, and the days and fraction of the full moon after the equinox, and the 
days of AC. SC. and from the sum subtract Jan. 80, and the remainder will be 
the AC. Index. 

(4§). Contra. NS. Table II. gives the indexes differing from AC. Indexes 
throughout the table. It makes the next great lunar cycle begin in AD. 8500, 
when AC. makes the next full moon of GN, 3 fall 3.2312 days after the equinox. 
And in the beginning of the present century, AD. =1807, GN. 3, its Index makes 
the full moon of Nisan fall on March 22, while AC. Index 3 makes it fall on 
March 24. 

(49). JSfbio. AC. Index and fraction added to March 21 AC. , gives the date of 
the full moon of Nisan in the year GN 3 (if that be the centurial year) in maxi- 
mum Hebrew time, in precise accordance with a mean year of 365.242,216 days, 
and a mean lunation of 29.530,589 days. AC. SC. does not always make the equi- 
nox fall on March 21. But that does not affect the accuracy of the lunar date, 
when the Index is added to March 21 AC, since every day added to AC SC. adds 
one day to the Index and one day to the date of the full moon, which is the sum 
of the date of the equinox of the moon after the equinox. (12.) 

(50). Then in AD. 1807=GN. 3, full moon fell Jan. 70.154,348 in minimum 
standard time OS. Add 1.098,148 for maximum Hebrew and 12 days NS. SC, or 
AC. SC, makes March 24.252,496 AC. or NS. And 1807 is the third year after 
leap year, when the maximum and the actual dates are the same. Then add 7 

17- 



AC. NOTES. 

years recession since AD. 1800 at the rate of 0.003,241 per year makes the date in 
AD. 1800 March 24.275,183. And in AD. 1800 the Index 3.2752 added to March 
21 makes March 24.2752, which is the same as found by direct calculation of the 
date of full moon. (32, 36.) 

(51). And Table C shows that from AD. 1800 to 1818, NS. uniformly makes the 
dates earlier than the astronomic dates, so as to make Easter fall on the forbidden 
day of full moon when that falls on Sunday, as shown in AC. 1st, 2d, and 3d Ex. 
(72, 73, 89.) 

AC. Rules Explained. 

(52). As to AG. Bule 1. In AC. Table I. the dates are one day less than given by 
AC. Rules 2, 3, 4, in order to reduce maximum Hebrew time in the beginning of 
the century to average standard time in the middle of the century. Then AC. In- 
dex gives the latest date upon which the full moon can fall when given in terms of 
the Egyptian rules. The comparison of the dates given by these rules with the 
astronomic dates in maximum Hebrew time for the 20 years from AD. 1800 to 1819 
in Table C shows that the Egyptian dates of GN. AC. average 0.29 day more than 
the astronomic dates. Therefore, subtract 0.29 for the average. And subtract 
0.162 for the recession for 50 years. And subtract 1.098,148 to reduce maximum 
Hebrew to minimum standard date. These make 1.550 to be subtracted for mini- 
mum standard date in the middle of the century. Then to minimum date add 0.50 
JCC. for medium date in the second year after leap year leaves 1.05 to be sub 
traded, or 0.05 more than by AC. Rule 1. (28, 89.) 

(53). In general terms, AC. Rule 1 directs that all the GN. shall be kept at the 
same distance from the standard GN. 3. This is now at March 23. And being 
always one day earlier than the full moon of Msan, its earliest date will be March 
20 and latest April 18. Then each GN. in succession will fall one day later than 
Dec. 31= Jan. 1, with one year added to the GN., until GN. 19 falls one day later 
than Dec. 31. But at the end of the year GN. 19 there is an intercalary, so that 
GN. 19 must remain at Dec. 31 until GN. 11 falls on Dec. 31, and then GN. 19 
becomes GN. 1 Jan. 1. (26.) 

(54). The main object of this table is to illustrate the Egyptian rules, which 
have governed the whole Christian Church since their adoption in the century after 
the Council of Nicea in AD. 325. The precise date of full moon for all time can 
be easily found by MDT. or MDB. But this table, without calculation (except to 
find GN. of the year by AC. Rule 1), will for all time give a near approximation 
to those dates. In the north of Europe the Alexandrian cycle (JE. Table) is indi- 
cated by notches cut in walking-sticks, which are called Clogs, Runstocks, Rum- 
staffs, Reinstocks, Runici, Primsteries, Scipiones, Baculi, Annales, Staves, Stakes 
(Brady, p. 47 ; Hone's Preface ; Rees' Runic Staff.) (18, 28.) (GND. Note 4.) 

(55). As to AG. Bule 2. Ninety-nine lunations are about a day and a half more 
than 8 Julian years. Hence to count by half days the rule would be : Add 8 in a 
circle of 19 to the GN. and a day and a half to the date. But to count by whole 
days, the Egyptian rules make the small GN. from 1 to 8 to be half a day earlier, 
and the large GN. from 9 to 19 to be half a day later than the average. Hence 30 
days are required to contain the series if it begin with a small GN., but 29 days if 
it begin with a large GN. (18, 66-70.) 

(56). Also, with any standard GN. and date, this rule will give every date in 
AC. Table I;, with this proviso : "When passing the junction, subtract one day 

18 



AC. NOTES. 

from the date, so as to bring the large GN. at one day after the small GN., as at 
Feb. 12, April 28, June 21, Aug. 19, Oct. 17, Dec. 15. (18-26, 66-70.) 

(57). As to AG. Bule 3. The years of construction of AC. Table I. are 365 days 
each, excepting GIST. 19, which with the intercalary is 366 days. Then a common 
year of 12 months alternately 30 and 29 days=354 days. Hence each year of 12 
months will recede 11 days, except GN. 19 will recede 12 days. And since this 
falls in the next year, one year is added to the GN. Then if these 12 months do 
not come within the limits, the year is embolismic, and 30 days are added, be- 
cause the 18th month always contains 30 days. (17, 23-26.) 

(58). And this rule will give every date in AC. Table I., provided that when the 
recession carries the date past the junction from a long month into a short month, 
one day must be added to bring the small GN. at the end of the short month, one 
day before the large GN. at the beginning of the long month. (19, 66-70.) 

(59). As to AG. Rule 4. The key date is the zero of the cycle, and one day less 
than the date of GN. 19, so as to omit the intercalary. Or it is an epact more than the 
date of GN. 1. Then multiply any GN. by 11 to find how many days the date has 
receded. And divide by 30 to find how many days the embolismic months of 30 
days have added, and the remainder is the recession from zero, which subtracted 
from the key date, gives the date of that GN. (17, 23-26, 57.) (MDC. Rule 1.) 

(60). And the key date for any series of GN. in AC. Table I., can be thus found. 
Multiply any GN. by 11 ; divide P by 30 ; add R to the date of that GN., and S= 
the key date— provided as before, if the key date be obtained from a GN. on one 
side of the junction, and the date of the GN. fall on the other, then if the date fall 
in the short month one day must be added, but if in the long month, one day must 
be subtracted to bring the large GN. at the beginning of the long month only one 
day after the small GN. at the end of the short month. (18, 19, 66-70.) 

(61). As to AG. Bule 5. Epacts are actual dates, in the reverse order. The key 
epact is the zero of the cycle as the key date is the zero of the cycle. Both fall at 
the same date. And since Epacts increase as dates decrease, and as both omit the 
intercalary, so the key epact is one day more than the Epact of GN. 19, as the key 
date is one day less than the date of GN. 19. (17, 18, 30, 57, 81, 120-130.) 

(62). And the key Epact can be thus found : Multiply any GN. by 11 ; divide P 
by 30 ; subtract R from the Epact of that GN., and R=key Epact. 

(63). In each great lunar cycle of 6501 years, there are 80 series of 19 epacts or 
570 Epacts of GN. to be found, as there are 570 dates of GN. to be found for the 
full moons of Nisan. These Epacts can all be found by AC. Rule 5, as the dates 
can all be found by AC. Rule 1 or 2, or 3, or 4. And the same rules modified by 
Contra Rule 8, will give all these epacts and dates, according to the Gregorian 
Calendar (NS.). And these rules, with AC. Rules 9 and 10, can easily be memo- 
rized. But for ordinary use it is more convenient to find the dates and the epacts 
from the Anglican Tables III. and IV. , with the column of Epacts which were 
added by BA. in 1874. (30, 120-130.) 

(64). As to AG. Bule 6. For AC. Table III. the figure O, placed under each 
GN., shows that when AC. Table II. makes the index to be O, then GN. 3 will 
fall on March 21, and from this standard the Egyptian rules AC. Rules 2 to 5, will 
give the date of each GN. that is opposite to O. And the date gives the Sunday 
letter and the Epact. Then for every day that GN. 3 advances, all the other GN. 
advance one day in a circle of 30 days on or between March 21 and April 19. Each 

19 



AC. NOTES. 

GN. in its turn will fall on April 19. The next advance of one day will make that 
moon fall on April 20, and thus become the full moon of Zif , at the same time that 
a full moon one lunation earlier in the same year will fall on March 21 and become 
the full moon of Nisan. This can be seen more distinctly in AC. Table I. And 
that table can be used instead of AC. Table III. But AC. Table III. in the An- 
glican form, is more convenient, for the single purpose of determining the date of 
Easter. And for that purpose, neither Table I. nor III., nor IV. is necessary 
either for AC, or for NS. The whole system of AC. is contained in AC. Table 
II. and Rule 1 or 2, or 3, or 4. And the whole system of NS. is contained in jSTS. 
Table II., with the same rules modified by Contra Eule 8. (66-70, 120-130.) 

(65). As to AG. Bide 7. AC. Table IV. is an extract from AC. Table I. or III., 
for present use, to facilitate the calculation of Easter. NS. Table IV. is collated 
with AC. Table IV., to show the difference by examples. 

(66). As to Contra Rule 8. The differences between AC. Table II., and NS. 
Table II., have been shown above (40, 48-51). Then as to NS. Retractions : AC. 
Rule 2 shows that the Egyptian rules put the dates of the small GN. from 1 to 8, 
half a day too early for the average, and the large GN. from 9 to 19 half a day later 
than the average. Hence when a small GN. begins the series, the last will fall on 
the 30th day. But when a large GN. begins the series the last will fall on the 29th 
day. Then NS. Table II. puts each GN. in its turn upon March 21 and 22. And 
when a small GN. falls on March 21 or a large GN. on March 22, the Egyptian 
date of the last of the series is April 19, and AC. leaves it there. (55-65.) 

(67). But NS. retracts to April 18, all GN. which regularly fall on April 19. 
And if this be GN. 1 to 8, then GN. 12 to 19 falls regularly on April 18. And to 
prevent two GN. falling on the same day, GN. 12 to 19 is retracted to April 17, and 
the whole series is crowded into 28 days. (66-70.) 

(6§). Now in Table C, GN. AC. , compared with the astronomic dates, show 
that when all the other dates are correct, the retraction of one day from the date of 
many of these GN. , would make it one day less than the astronomic date of full 
moon, and thus bring Easter on the forbidden 14th Nisan when the full moon falls 
on Sunday. And the dates of GN. NS. being two days earlier than the dates of 
GN. AC, these dates, if retracted one day, would in all cases make the date two 
days before the date of full moon, and thus bring Easter on the forbidden 14th 
Nisan, when the dates fall on Saturday or Friday, and in many cases when they 
fall even on Thursday. (89.) 

(69). The origin of these retractions is shown in Table A. The Alexandrian 
cycle gave the true dates of new moon about AD. 325 as nearly as practicable in 
the simple form of that calendar. But it paid no regard to the solar dates of the 
new moons of Nisan, and put the junction of the long month at GN. 16 April 6. 
Then Dionysius added 13 days to all the dates. This would have brought the ir- 
regularity at the junction at April 19. And April 19 would have been the begin- 
ning of the next lunar month. To avoid this irregularity, all GN. which regularly 
fall on April 19 are retracted to April 18. And this is founded upon the double 
error of omitting the earliest new moon of Nisan GN. 8 March 6, and then adding 
13 days instead of 15 days for the dates of full moon as shown in Table B, where 
it is shown that if Dionysius had begun with GN. 8 March 6 and had added 15 
days to the dates, his table would have given the true dates of the full moons of 
Nisan on and between March 21 and April 19, and the irregularity at the Junction 
would have fallen at GN. 16 April 21, (19, 20, 55, 81, 85.) 

20 



AC. NOTES. 

(70). Hence, these NS. Retractions to keep the dates within the "paschal limits" 
March 21 and April 18, are founded upon the double error of Dionysius, and are 
astronomically false, and bring Easter on the forbidden 14th Nisan. (19, 20, 55. 
66-70, 81, 85.) 

(71). As to AC. Bides 9, 10. Memorize Rules 9 and 10 to find the day of the 
week corresponding with any day of the month dated NS. And Rule 1, to find 
GN., and Rule 4 to find the date of GN. from the key date March 55 during this 
century (and March 58 from March 1 AD. 1900 to March 1 AD. 2100), and then 
find NS. Easter on Sunday next thereafter. And add one day to the date of GN. 
thus found for the average date of full moon, and for other dates of full moon add 
or subtract periods of 29£ days. But for full moon omit Contra Rule 8. (68.) 

(72). As to 1st and 2d Examples. Lindo mentions these years in which Easter 
and the Passover fall on the same day. In both years it was the day of full moon 
which was forbidden by the Council of Nicea, while by the Mosaic rule, the Pass- 
over could not possibly fall on the day of full moon. And Table C shows that in 
the beginning of this century GN. NS. fell one and two days before the maximum 
Hebrew date of full moon, so as to bring Easter on the forbidden 14th Nisan when 
the date of GN. NS. fell on Friday or Saturday. (6-11, 77, 89.) 

(73.) As to 3d Example. Professor De Morgan, Book of Almanacs, Introduction, 
p. viii., says : "When it happens that Easter Day falls on the day of real full moon, 
the apparent contradiction always makes a stir. On the last occasion, in 1845, I 

wrote an account of the Gregorian Calendar {Companion to the Almanac 

for 1845)." (80 bis). 

(74). As to Uh Example. This Greek Easter is referred to by Dr. Hill. This is 
GN AM. 19. And Table C shows that the Greeks always hold Easter in the month 
Zif in each GN. AM. 19, 5, 8, 11, 16. (92, 108-119.) 

GENERAL REMARKS AND CONTRADICTIONS 

AS TO THE 14TH DAY OF NlSAIT. 

(75). The day of full moon, 'on or next after the vernal equinox, is accounted the 
14th day of Nisan, upon which Easter must not be held according to the decision 
of the Council of Nicea. And this assumption is based upon the Paschal Canons 
and their history, and the Mosaic ruin as stated by Maimonides, and the historic 
facts stated by Joscphus, and the present Hebrew Calendar when interpreted by the 
Mosaic rule. (1-11.) 

(76). Contra. Maimonides, Scaliger, Muler, Lindo, Nesselman, Slonenski, and 
Sekles, give rules to simplify the calculations by the present Hebrew Calendar (HC.) 
which is the most occult and most complicated of all calendars. But no known 
author except Maimonides, states the general principle of the present custom. He 
says (Col. 280) : " If the date fall a moment before noon, the calendar is celebrated 
on that day." Calculation shows that this is the date of mean conjunction counted 
in Hebrew time with great accuracy. This makes Nisan begin before conjunction, 
and full moon to fall on the day of the Passover. And such is the present custom. 
And these were impossible under the Mosaic rule. (6-8.) 

(77). No known author has objected to this interpretation. And Lindo says that 
his calculations have been examined by Airy the astronomer and found to be cor 
rect, and that his work has been approved by distinguished Rabbis in Great Britain. 

21 



AC. NOTES. 

And I suppose that his work is now the standard Hebrew authority in the English 
language. In his introduction he says : " The Council of Nice ordered that Easter 
should not be held on the first day of the Passover, ' ne videantur Judaizare.' But 
in 1825 and 1903 both fell on the same day." And AC. 1st and 2d Examples, show 
that both fell on the day of full moon. (1, 3, 72.) 

(7§.) And Table C shows that the Gregorian Calendar (NS.) frequently puts 
Easter on the day of full moon by dating GN. NS. one and two days before the 
date of full moon. And Aloysius, Lilius, Christoph Clavius, Petrus Ciaconius, 
and others (Anthon), spent ten years in framing that calendar. Long (1267). And 
Delanibre (V. 1, p. 12) says : " I found the calendar better than its authors supposed. " 
But Long (1267) says that Lilius explains the system and defends it from the attacks 
of Mcestlinus, Scaliger, and Vieta. 

(79). And the Dionysian Cycle (OS.) governed the whole Christian Church for 
more than a thousand years (AD. 534 to 1582), and now governs the Greek Church 
in a Greek form. And Table B shows that it gave the dates of the GN. one and two 
days before the actual date of full moon, about AD. 325 (as NS. does at present). 
But no known author has made any objections on this score. On the contrary, 
NS. does the same. (85, 89.) 

(80). Now. Notwithstanding this imposing array to the contrary, the reasons 
above given have been considered sufficient for the assumption that the ancient 
rule made the day of full moon to be the 14th Nisan, upon which the Passover 
could not possibly fall, when modifying the present rules (HC.) so as to give an 
cient Hebrew dates correctly (HCM.). And for the same reason, AC. Indexes pre 
vent Easter falling on the same day as full moon. And for this purpose the dates 
are given in maximum time, which is the true time in the third year after leap year, 
and in Hebrew time counted from 6 hours before midnight at Jerusalem, since the 
14th ISTisan is a Hebrew date. And March 21 of the Paschal Canons is not the act- 
ual date of the vernal equinox in AD. 325, when it actually fell on March 20. But 
it was the date of the vernal equinox in each third year after bissextile about that 
time. (1-16, 75-80.) (HC. Note 178.) 

(§0 bis). Blunt (p. 27) says: "The rule for finding Easter (founded on the 
decree of the Council of Nicaea) is not quite exactly stated. Instead of full moon, 
it ought to say, the 14th day of the calendar moon, whether that be the actual full 
moon or not. In some years (as in 1818 and 1845) the full moon and Easter coincide, 
and the rule then contradicts the tables." (72, 73.) 

Also. Brady (p. 296) says, that in 1810 the moon was full at 3 A.M. on March 
21 ; but according to lunar computation it was full on the 20th, and Easter was 
April 22, and not March 25. (72, 73. ) 



AC. NOTES. 



(81). 



Table A. 





Alexandrian Cycle of AD 425. 




Dionysian 


Cyclo of 


AD. 

Coinci- 
dence. 


Roman Epac 


3 of AD. 1582. 




AD. 534 


(OS.). 


Month. 


GN. 
16 


Epacts. 


Month. 


GN. 


Epacts. 


Month. 


GN. 
16 


Ep. 1874. 


6419 


Feb. 6 


23 


Mar. 8 


16 


23 


Mar. 21 


23 


6077 


" 7 


5 


22 


" 9 


5 


22 


" 22 


5 


22 




" 8 




21 


" 10 




21 


" 23 




21 


5735 


" 9 


13 


20 


" 11 


13 


20 


" 24 


13 


20 


5893 


" 10 


2 


19 


" 12 


2 


19 


" 25 


2 


19 




" 11 




18 


" 13 




18 


" 26 




18 


5051 


" 12 


10 


17 


" 14 


10 


17 


» 27 


10 


17 




" 13 




16 


" 15 




16 


" 28 




16 


4709 


" 14 


18 


15 


" 16 


18 


15 


" 29 


18 


15 


4367 


" 15 


7 


14 


" 17 


7 


14 


" 30 


7 


14 




" 16 




13 


" 18 




13 


" 31 




13 


4025 


" 17 


15 


12 


" 19 


15 


12 


April 1 


15 


12 


3683 


" 18 


4 


11 


" 20 


4 


11 


" 2 


4 


11 




" 19 




10 


" 21 




10 


" 3 




10 


3340 


" 20 


12 


9 


" 22 


12 


9 


" 4 


12 


9 


2998 


" 21 


1 


8 


" 23 


1 


8 


" 5 


1 


8 




" 22 




7 


" 24 




7 


" 6 




7 


2656 


" 23 


9 


6 


" 25 


9 


6 


" 7 


9 


6 




" 24 




5 


" 26 




5 


" 8 




5 


2314 


" 25 


17 


4 


tt 27 


17 


4 


" 9 


17 


4 


1972 


" 26 


6 


3 


" 28 


6 


3 


" 10 


6 


3 




" 27 




2 


" 29 




2 


" 11 




2 


1630 


" 28 


14 


1 


" 30 


14 


1 


" 12 


14 


1 


1288 


Mar. 1 


3 


* 


" 31 


3 


* 


" 13 


3 


* 




" 2 




29 


April 1 




29 


" 14 




29 


946 


" 3 


11 


28 


" 2 


11 


28 


" 15 


11 


28 




« 4 




27 


" 3 




27 


il 16 




27 


604 


" 5 


19 


26- 


" 4 


19 


26 (25) 


" 17 


19 


26 (25) 


261 


" 6 


8 


25 (25) 


" 5 


8 


25, 24 


" 18 


8 


25, 24 


- 


" 7 




24 


" 6 

„ 7 


16 
5 


23 

22 









(82). Explanation. The first column gives the years in which the opposite GN. 
of new moons from GN. 16 Feb. 6 to GN. 8 Mar. 6 become the new moons of 
Nisan, and GN. 16 Mar. 8 to GN. 8 April 5 become the new moons of Zif, and 
GN. 16 Mar. 21 to GN. 8 April 18 become the full moons of Zif. This is explained 
in MDT. Mosaic (A). (102-104.) 

(83). GN. 16 Feb. 6 to GN. 5 April 7, with the epacts, are extracts from JE. 
Table. (69, 85, 89, 120-130.) 

(84). The Dionysian cycle is given as a separate calendar (OS.). The epacts in 
this form were added in 1874 by B. A. See Tables B. and C. (29 30 102-104, 
108-130.) 



23 



AC. NOTES. 



Table B. 

(85). Explanation. The 2d and 
3d cols, give the GIST, and dates of 
new moon in the day of March, as 
copied from the Alexandrian cycle 
in Table A. (81.) 

(§6). The 4th col. gives the as- 
tronomic dates of the full moon in 
the 19 years beginning AD. 825 in 
maximum Hebrew time next after 
the vernal equinox, which in AD. 
325 fell March 21.430,734 in maxi- 
mum Hebrew time. (14-16.) 

(§7). The 5th col. gives the true 
date of the GN. for full moon 15 
days later than the Egyptian dates 
of new moon. And they could not 
be less without being less than the 
astronomic dates in 15 of the 19 
years, and thus bringing Easter on 
the forbidden day of full moon, 
when that fell on Sunday. And 
full moon is 14.765 days after new 
moon. And this table proves that 
the Alexandrian cycle gave the cor- 
rect dates of new moon in maxi- 
mum Hebrew time in the 19 years 
beginning AD. 825. And this makes the true . Paschal limits, about AD. 325, to 
be March 21 and April 19. (66-70, 102-104.) 

(§§). The last column contains the Dionysian dates corresponding with GN. 
OS., as copied from the Old Style Western Calendar (OS.) and with GIST. AM., as 
copied from the present Greek Calendar (AM.). And this shows that Dionysius 
omitted GIST. 8 March 6, which had been the new moon of Nisan since AD. 261, as 
shown by the first column in Table A (and in MDT. Mosaic, where the principle is 
explained), and included GN. 8 April 5 in Table A, which had been the new moon 
of Zif since AD. 261. And then beginning with GN. 16, March 8, which was the 
second in the series of the new moons of Msan, he added 13 days to the dates, and 
thus made all the dates two days less than the true dates, and invariably brought 
Easter on the day of full moon, when that fell on Sunday. Thus, by including 
the new moon of Zif GN". 8 April 5, and by counting the days two days too early 
for the astronomic dates of the full moons of Nisan, Dionysius made the "Paschal 
limits " March 21 and April 18. And this calendar was adopted by the Council of 
Chalcedon in AD. 534. And it governed the whole Christian Church until AD. 
1582, and now governs the Eusso-Greek Church (AM.) in a Greek form. In both 
forms the consequence is shown in Table C. (66-70, 81, 89, 102-104.) 





a 


£ 




Jz5 










•S 


<D 




O 








Q 


X 






o 






TO 

Q 


< 


o> 


'■a 


c£ 


o3 


CD 


!>! 




m 


< 


c3 


oW 


Q 


O 


< 






ti 


X 


w e3 




ti 


£ 


o 


1* 


& 


5 


<& 


H 


o 


o 


B 


330 


8 


6 


21.703 


21 


338 


16 


8 


23.231 


23 


16 


13 


21 


327 


5 


9 


24.821 


24 


5 


2 


22 


335 


13 


11 


26.349 


26 


13 


10 


24 


343 


2 


12 


27.877 


27 


2 


18 


25 


332 


10 


14 


29.467 


29 


10 


7 


27 


340 


18 


16 


30.996 


31 


18 


15 


29 


329 


7 


17 


32.586, 


32 


7 


4 


30 


837 


15 


19 


34.114 


34 


15 


12 


32 


326 


4 


20 


35.704 


35 


4 


1 


33 


334 


12 


22 


37.232 


37 


12 


9 


35 


342 


1 


23 


38.780 


38 


1 


17 


36 


331 


9 


25 


40.350 


40 


9 


6 


38 


339 


17 


27 


41.879 


42 


17 


14 


40 


328 


6 


28 


43.469 


43 


6 


3 


41 


336 


14 


80 


44.997 


45 


14 


11 


43 


325 


3 


31 


48.587 


46 


3 


19 


44 


333 


11 


33 


48.115 


48 


11 


8 


48 


341 


19 


85 


49.643 


50 


19 


16 


48 


330 


8 


38 


21.703 


21 


8 


5 


49 



24 



AC. NOTES. 



(§9). 



TABLE C. 



"3 

S3 






m 
















© 






"6 
o 






O 
m 


o" 


OQ 


od 




a 


d 




O 




d 


o 








<3 


fc 

£ 


O 




< 






© o 


l-M 


H 
ti 


<J S 




^ M-l 


< 


o 


O 


o 


S 

< 


$ 


H 


P 


r^H 


o 


O 


GO § 




■S3 


o 


«4H 

o 


=4-1 

o 


o 


o 


O 


<! 


*££ 


o 


O 






fri 


fc 


c3 


c3 


o 

e3 


fc 


© 
-4-= 
C3 


Jzq 


© 


££ 


© 

c5 


© 


H 




p 


O 





ft 


P 


GN. 
19 


p 

AM. 

58 


O 


h 


P 


ft 


p 


AD. 


Mar. 


GK 


AC. 


NS. 


OS. 


GK 


AD. 


March. 


HCM. 


HC. 


1288 


1807 


24.25 


3 


24 


22 


56 


1 


1883 


24.01 


24 


52 


3683 


1808 


42.90 


4 


43 


41 


45 


1 


45 


2 


1884 


41.90 


41 


40 


6077 


1809 


32.02 


5 


32 


30 


34 


2 


34 


3 


1885 


31.27 


31 


30 


1972 


1810 


50.66 


6 


21 


49 


53 


3 


53 


4 


1886 


50.17 


50 A 


48 G 


4367 


1811 


39.78 


7 


40 


38 


42 


4 


42 


5 


1887 


39.54 


39 A 


88 A 


261 


1812 


28.90 


8 


29 


27 


61 


5 


61 


6 


1888 


27.90 


27 


26 


2656 


1813 


47.55 


9 


48 


46 


50 


6 


50 


7 


1889 


46.80 


46 A 


45 A 


15051 


1814 


36.66 


10 


37 


35 


39 


7 


39 


8 


1890 


36.17 


38 


34 A 


i 946 


1815 


25.78 


11 


26 


24 


58 


8 


58 


9 


1891 


25.53 


25 A 


53 


3340 


1816 


44.43 


12 


45 


43 


47 


9 


47 


10 


1892 


43.43 


43 


42 


15735 


1817 


33.55 


13 


34 


32 


36 


10 


36 


11 


1893 


32.80 


82 


81 


'1630 


1818 


22.66 


14 


23 


21 


55 


11 


55 


12 


1894 


22.17 


22 


50 A 


'4025 


1800 


41.37 


15 


42 


40 


44 


12 


44 


13 


1895 


41.03 


41 A 


39 


16419 


1801 


30.49 


16 


31 


29 


33 


13 


33 


14 


1896 


29.43 


29 


28 


2314 


1802 


49.14 


17 


50 


48 


52 


14 


52 


15 


1897 


48.33 


43 


47 


4709 


1803 


38.25 


18 


39 


37 


41 


15 


41 


16 


1898 


37.70 


37 A 


36 A 


604 


1804 


27.37 


19 


28 


26 


60 


16 


60 


17 


1899 


27.08 


27 A 


25 


2998 


1805 


46.02 


1 


46 


44 


48 


17 


48 


18 


1900 


45.93 


46 


44 


5393 


1806 


35.14 


2 


35 


33 


37 


18 


37 


19 


1901 


35.33 


35 


34 


1288 


1807 


24.25 


3 


24 


22 


56 


19 


56 


1 


1902 


24.69 


24 A 


52 




Q 


tfDT. 4th 


5th Ex.) 










2 


1903 


43.59 







(90). Explanation of Table C. The first column is the same as the first column 
in Table A, and all the GN. on the same line refer to the same moon under differ- 
ent GN., at the beginning and end of the present century. (81.) 

(91). The dates of full moon from 1800 to 1818 are in maximum Hebrew time 
in the beginning of the century, to compare with dates by AC. Table II., and by 
NS. Table II., and by OS., and by AM. They refer to the same GK on the same 
lines from 1883 to 1902, in which the dates are in Hebrew Calendar time to com- 
pare with dates by HCM. and by HC, because those dates are astronomic. (31- 
51, 85.) 

(92). The dates of GK OS., and of GK AM., are the same as in Tables A and 
B, and in the separate calendars OS. and AM., with the addition of 12 days NS. 
SC. (81, 85, 102-104, 126.) 

(93). The dates of HCM. are taken from HCM. Table, thus : By HCM. Rule 1, 
count the Hebrew days as beginning in the evening after noon of the dates found 

25 



?A 



AC. NOTES. 

by rule. And the dates of HC. are taken from HC. Table, by HC. Rule 1 count- 
ing the Hebrew day as beginning in the evening before noon of the dates found by 
rule. Then in both cases take the date one day less and mark it A when A adds 
one day to the astronomic date, and subtract two days and mark the date G-, when 
G adds two days to the astronomic dates. And these Hebrew dates are counted by 
Hebrew lunations, which in 1883 make the dates count 0.078,167 more than by 
mean lunations. And when this is added to March 45.96 in AD. 1900, all the 
dates of GN. HCM. agree precisely with the astronomic dates. (1-11, 75-77 ; HO. 
Notes 157-163.) 

Alexandrian Canon. 

(94). The lunar portion of the Alexandrian Canon was the Alexandrian Cycle 
which gave the correct dates of the 235 new moons in 19 years about the time of 
the Council of Nicea AD. 325. The solar portion was the Paschal Canons, to 
define which of these new moons was to be counted the new moon of Nisan, from 
which to determine the date of Easter. This was adopted as the first Christian 
Calendar in the century after the Council of Nicea in AD. 325, as a substitute for 
the annual prediction of the time of Easter, by Egyptian astronomers. (1-5, 
94-107.) 

(95). Contra. First. As to the origin of the Alexandrian Cycle. Jarvis (p. 87- 
92) gives the whole of this cycle (JE. Table) of which a part is given in Table A. 
He calls it "The Calendar of the Ancient Church, established by the Council of 
Nice." And the remarks by Dr. Hill of Athens, and the Archbishop of Corinth, 
indicate that they believe it to be the "Ordinance of the Council." And Rees 
(Canon Paschal) and the Encyclopedia Britannica say that it is attributed to Euse- 
bius of Csesarea, and to have been constructed by order of the Council of Nicea- 
(1-11, 17-26, 81, 108-119.) 

(96). Now : Delambre (Vol. 1, p. 2) says : " The Council of Nice supposed 

that the equinox remained invariably fixed on the 21st March as they found it in 
the year 325. There does not in fact exist any decree or any act of this Council. 
Their rule for the celebration of Easter is not found except in a letter, which the 
Fathers addressed to the Church in Alexandria. The letter itself does not exist ; 
we do not know the dispositions, except from the testimony of certain authors 
who report the spirit without citing the precise expressions. According to these 
authors, the Paschal moon was that of which the 14th day coincides with the ver- 
nal equinox or the next thereafter. And Easter day is Sunday next after the 
Paschal moon." And Long (Sec. 1255) says : " This determination is not among 
the Canons of the Council, but may be seen in their Synodic Epistles, preserved to 
us by the two ecclesiastical historians, Socrates and Theodoret." Neale (p. 113) 
and Seabury (p. 76) say : ' ' No such canons are found among the proceedings of 
the Council." And " The Patriarch of Alexandria was commissioned to announce 
the time of Easter.". And Brady (p. j$$4) says that most of the Churches used the 
ancient Jewish cycle of 84 years. And Seabury (p. 78) quotes Prideaux to the 
same effect. (81, 94, 95, 108-119.) 

(97). Also : From internal evidence, there are several reasons for inferring, that 
the Alexandrian Cycle was the Egyptian substitute for the modern almanac for 
the sole purpose of giving the dates of the 235 moons in the cycle, and that it was 
adopted by the Christians to determine the dates of the full moons of Nisan, 

26 



AC. NOTES. 

because it gave correctly the dates of new moon about AD. 325. Thus 1st. We 
know that such was the use of the Egyptian Cycle, which Sosigenes, the author of 
the Julian Calendar, adapted to Roman dates. And one of them cut in stone can 
now be seen in the National Museum at Rome. (JE. Table). This has GN. 1 at 
Jan. 1. History and calculation make new moon fall on Jan. 1 in BC. 45, when 
the Julian Calendar was inaugurated. Hence BC. 45=GN. 1, and that makes 
AD. 325 =GN. 9. And GIST. 9 is dated April 1st, while in AD. 325 new moon fell 
March 31, and the Alexandrian Cycle gives March 31 for GN. 3. But lunar dates 
recede 0.002,241 day per year, and from BC. 45 to AD. 325, the date of the Roman 
moon GN. 9 had receded 1.20 day and fell on March 31. But the Alexandrian 
Cycle gave the date of GN. 3 as March 31. So that the Christians abandoned the 
old Roman Cycle which no longer gave correct dates, and adopted the Alexandrian 
Cycle which did give correct dates and made AD. 325 to be GN. 3. And from 
that day to the present all the cycles used by the Westerns have made AD. 325= 
GN. 3. And Delambre (Vol. 1, p. 37) says : " The Alexandrians gave the golden 
number one to March 23, because that was at that time the date of the vernal equi- 
nox, and it resulted that Jan. 1st was the golden number three." If this be so, 
then the Alexandrian Cycle must have been constructed about 250 years before 
AD. 325 when the vernal equinox fell as late in Roman time as March 23, since it 
receded at the rate of 0.7784 day per century. (1-5, 32, 36, 37, 81, 85. GND. and 
Epacts.) 

(98). Now : If this cycle had been prepared by order of the Council, it certainly 
would not have had GN. 1 dated March 23, because that was the date of the vernal 
equinox, since the paschal canons say, that " the 21st day of March shall be 
accounted the vernal equinox." And we would suppose that they would have 
retained the similar Egyptian cycle in the Julian Calendar which makes AD. 
325 =GN. 9, with the correction of one day to make GN. 9 fall on March 31. Or 
else they would have made the year of the Council the first year of the cycle, and 
would have marked the date of new moon which fell on March 31 in the year 
of the Council with GN. 1. But they did neither. 3d. This Alexandrian cycle 
has no obvious connection with the date of Easter. It gives the dates of new moon 
from which the dates of the full moons of Nisan might be found by adding 15 days 
to find the full moon, on or next after March 21 of the paschal canous. And this 
created confusion, since some added 12, and others 13, and others 14 days. 4th. 
Table A shows that it pays no regard to the solar dates. GN. 8 March G had been 
the new moon of Nisan since AD. 281, and GN. 8 April 5 had been the new moon 
of Zif since AD. 261. But GN. 8 March 6 is put in the previous month, and GN. 
8 April 5 is put at the end of the remaining new moons of Nisan. (81, 82, 99, 
101-106.) 

(99). Contra. Second. As to the Cycle itself. Jarvis (pp. 94, 95), after de- 
scribing the Egyptian cycle in the Julian Calendar (JE. Table), continues : " The 
computists of the Council of Nice proceeded in a similar manner, but with a differ- 
ent object. The precession of the equinoxes had in the interval of time shifted the 
cardinal points in the zodiac, so that the winter solstice had passed from the 25th 
to the 21st of December, and the vernal equinox from the 25th to the 21st of March. 
The object of the Council was to determine the day of the paschal full moon, and 
to establish a rule for the computation of Easter. They found that the first new 
moon after the vernal equinox in the year of their session, fell on the 23d March. 

27 



AC. NOTES. 

They made it, therefore, the beginning of a new cycle of 19 years, and consequently 
marked it with the golden number one. It is possible that in the ordinary course 
of the Julian Calendar, the year of their session was the third of the Metonic cycle, 
but whether that was or was not the case, the result of placing the golden number 
one opposite to the 28d March was as follows :" 

(10®). Then follows the table. Then: " This mode of computation continued 
to be generally used in the Christian Church until the year AD. 1582, when .... 
Gregory XIII. published a bull abolishing the use of the calendar established by 
the Council of Nice, and substituting that which has since been called the Gre- 
gorian. In this the golden numbers were discontinued, and the system of epacts 
applied by Aloisi Lilio to the cycle of 19 years was adopted in its stead. Ten days 
were retrenched from the year on account of the precession of the equinoxes, to 
bring forward again the vernal equinox to the 21st March, and the 5th of Octo- 
ber was thenceforward to be called the 15th;" 

(101). Now : First. The precession of the equinoxes has no effect upon calendar 
dates. In Julian time the date of the equinox recedes 0.7784 day per century, 
because the Julian year of 865.25 days is 0.007784 day longer than the equinoxial 
year of 865.242,216 days. Second. Easter depends upon the date of the first full 
moon on or after the vernal equinox, and not ' ' the first new moon after the vernal 
equinox." Third. New Moon fell on March 31 in AD. 325. That is marked GN. 
3. Aud from that day to the present the Western rules have made AD. 825 to be 
GN. 3. But the Greek rules make it GN. 19. Fourth. The rules of the Julian 
Calendar make AD. 325 to be GN. 9. And that is marked April 1st (JE. Table). 
Because in Julian time the moon recedes 0.8241 day per century, and from BC. 45 
to AD. 325 it had receded 1.199 day. Fifth. The Metonic cycle (OE.) is funda- 
mentally different from the Egyptian cycle in the Julian Calendar. Sixth. This 
calendar was not " established by the Council of Nice," according to Delambre, 
Long, Neale, Seabury, Prideaux, and Brady. Seventh. The system of golden num- 
bers was not abolished. They do not appear in the Missal as connected with the 
cycle of Epacts. But in the explanatory tables, the epacts are shown to be derived 
from the golden numbers. And when they are collated with this cycle (JE. Table) 
they are seen to be substantially the dates of the golden numbers in the reverse 
order. And AC. Rule 5 proves it. (1, 29, 30, 32-36, 61-63, 81, 85, 89, 96, 120-13CU 

Dionysian Cycled OS. 

(102). This never gave the dates of the full moons of Nisan, in accordance with 
the Paschal Canons and with the decision of the Council of Nicea. Table A shows 
that at its inception, it omitted the new moon of Nisan GN. 8 March 6, and substi 
tuted the new moon of Zif GN. 8 April 5. Then for the dates of full moon it added 
13 days to the dates in the Alexandrian cycle, which were the dates of mean new 
moon about AD. 325, while full moon is 14.765 days later than new moon. And 
Table B shows that in most cases the dates of GN. OS. were two days before the 
date of full moon. And in all such cases it put Easter on the forbidden 14th Nisan, 
when these dates fell on Friday or Saturday, and full moon on Sunday. (1-11, 
81, 85.) 

(103). Thus : Table A shows that in AD. 261, the new moon of GN. 8 March 6 
became the new moon of Nisan ; and the moon one lunation later, GN. 8 April 5, 
became the new moon of Zif. Then AD. 273 =GN. 8 next after AD. 261. In 

28 



AC. NOTES. 

AD. 273, in Hebrew time the venial equinox fell March 21.836 and lull moon 
MarcK 21.387. This shows that the full moon of GX. 8 March 21 had just passed 
the vernal equinox into the month Xisan, and at the same time the new moon of 
GX. 8 April 5, passed into the month Zif. Then from March 21.387 subtract 
14.765, leaves March 6.622 as the date of the new moon of Xisan GX. 8 in Table A, 
which was omitted when OS. was formed, while the moon one lunation later GN. 8 
April 5 was substituted. (12, 13, 36, 81, 85.) 

(10-1). Also. Table C shows that at the present time GN. OS. substitutes,/?^ 
moons of Zif for five moons of Nisan, viz., in the years GN. OS. 8, 19, 11, 3, 14. 
And in this order the moons of Xisan passed into the month Zif in AD. 261, 604, 
946, 1288 and 1630. And GX. 6 will follow in AD. 1972. And AD. 6419 the 
Dionysian cycle will not have a single moon of Xisan left. This is shown by the 
first column of Table A. This is explained in MDT. (A) (81, 89.) And in The 
Churchman's Calendar for 1870 (pp. 39-43), William Moore, Esq., gives his calcu- 
lations of the dates of Easter NS. and OS. from 1753 to 2013. And these show 
that in the years GN. 3, 8, 11, 14, 19 Easter OS. falls 4 and 5 weeks later than 
Easter NS. But in the other years generally one week later, and sometimes on the 
same day. And Table C shows that in other years, the date of GN. OS. is 4 days 
later than the date of GN. NS. So that if the date of GN. NS. fall not later than 
Wednesday, both Easters will fall on the same day. 

History op the Dioxysian Cycle. 

(105). The Alexandrian Cycle gave the true dates of all new moons about AD. 
325 as above shown. But the Paschal Canons required the dates of the full moons 
of Xisan. Then says Brady (p. 294) : ' ' The full moon of Xisan was the 14th 

of the moon's appearance The Church of Rome changed its cycles in 

455, 457, 525, 1582." And Xeale (p. 113) says : " AD. 455 S. Pretorius gave Easter 
correctly April 24, but the Western Church held it April 17." And Seabury (pp. 
87, 88, 89) says: "In AD. 527 the Romans abandoned Xisan 16 as the earliest 
date of Easter, and following Dionysius adopted Xisan 15, as had previously been 
done by the Bishops of Alexandria, while the British and old Irish or Scotch had 
used Xisan 14." And Seabury (p. 78, quoting Prideaux) says : " Xo effectual 
cure was found till Dionysius Exiguus brought the entire Alexandrian Canon into 
the Roman Church, and this was adopted with entire unanimity," — i.e., the 
Paschal Canons and the 19 Alexandrian dates of new moons with the addition of 
13 days. (1, 81, 85.) 

(106). This cycle was adopted by the Council of Chalcedon in AD. 534. It is 
given by Wheatly (p. 38). It is given in the old Anglican Prayer Books (before 
1752 when the English adopted NS.), " To find Easter for ever." Anathema was 
pronounced against any who should find Easter by any other rule. It is given in 
this work as a separate calendar (OS.). It is given above in Tables A, and B, 
and C. $1, 85, 89.) (GXD.) 

(107). The statement above, that in AD. 527 the Romans followed Dionysius 
and adopted Xisan 15 as the earliest date of Easter, shows that the dates of GX. 
OS. were regarded as the dates of the 14th Xisan. But such was not the fact, 
according to the Mosaic rule which determined dates at the time of the Crucifixion 
;i-ll, 81, 85, 105.) 

29 



AC. NOTES. 

The Greek Calendar. 

{!©§). Tables B and C show that for the same years AD. the Greek Calendar 
(AM.) gives the same date of Easter as the Dionysian Calendar (OS.). The only 
difference is in the number of the year in the cycle. And to find that year add 
5508 to the year AD. for the year AM. (the " Constantinopolitan Period" analo- 
gous to JP. and used before JP.). Then divide the year AM. by the circle 19 and 
R=GN. AM. Consequently, all the remarks above, respecting the Dionysian 
Cycle apply to the present Greek Cycle. (85, 89, 102-107.) 

(109). Contra. First. The following are repeated in the Churchman's Calendar 
of 1866, 1867, 1868, viz.: " The following is the explanation concerning the Greek 
Easter, which was given to Dr. Hill, by Amphilochios, formerly a pupil in the 
American Mission School, and now Archbishop of Corinth. The Nicean rule is 
followed by the Anglican and the Greek Churches alike." 

(110). Now. This must signify that according to the Paschal Canons, both hold 
Easter on Sunday next after the date of GIST., which is next after March 21. This 
they both do. But the Greek March 21 is 12 days later than the Anglican March 
21, and falls on the Anglican April 2. (1, 74.) 

(113.'. Contra. Second. Dr. Hill continues: "But the Anglicans reckon the 
moon of Nisan by the full moon, so that a moon which is now in Adar (February) 
may be considered a moon of Nisan. The Greeks, however, insist that the moon 
of Nisan, must be the new moon in Nisan, and in this they are in strict accordance 
with Jewish usage." 

(112). Now. By the Mosaic rule the new moon of Nisan was used to find the 
full moon. By the present Hebrew rules (HC.) the new moon of Tisri, is used to 
find the full moon of Nisan. And the Alexandrian Cycle of new moons was used 
to find the full moons of Msan. These show "Jewish usage." But it is not 
obvious, what difference it makes, whether the date of full moon is given directly 
in the Anglican mode or whether it is found from the date of the new moon, pro- 
vided the dates agree. And some added 12, others 13, and others 14 days to the 
dates in the Alexandrian Cycle, until by common consent the Dionysian Cycle of 
full moons was adopted. And from this remark it would appear that the Athe- 
nians use the Alexandrian Cycle of new moons, and like Dionysius, add 13 days 
for the date of full moon, while others in the same Church, use the cycle of 
full moons as given in AM., since that was obtained from a Sclavonian Priest, and 
what is there copied as to the date of Easter, is from ' ' The full Christian Calendar, 
by the Metropolitan of Kiev." (6-8, 81, 105.) 

(113). Contra. Third. Dr. Hill continues : "Another rule operates, viz.: that 
when the Jewish Passover falls on Sunday, then the Easterns celebrate Easter on 
the Sunday following, and so it happened in 1864 that by these differences, and 
those of Old Style and New Style, the Greek Easter was five weeks later than ours, 
and fell on our 1st May, which with them was April 19." 

(114). Now. This Greek date of Easter April 19 OS. in 1864 is among the dates 
copied from the calendar by the Archbishop of Kiev. (AM.) In AC. 4th Example 
it is shown that this was 10 days after the date of full moon April 21.848. And 
that this was the Mosaic full moon of Zif, one month after the full moon of Nisan. 
And the same thing occurs in each 5 out of 19 years. AD. 1864= GN. AM. 19 
in Table C shows that the Greek Easter falls in the month Zif, in each GN. AM 
19, 5, §, 11, 16, for the reasons explained above. (36-40, 81, 82, 102-104, 116.) 

30 



AC. NOTES. 

(115). Contra. Fourth. Dr. Hill continues: "The Greek rule is undoubtedly 
the Nicean one, and should be our ecclesiastical law ; but the Western astronom- 
ical law (NS.) is scientifically correct. We suggest, the Greeks should adopt New 
Style, and the Anglicans their rule of Nisan, and there -will be a fair and orthodox 
adjustment of the difference. There should be, also, a prime meridian." 

(116). Now. It is not apparent how this could be done, since the whole object 
of the Gregorian Calendar was to correct the errors of the Dionysian Calendar. 
And the Greek Calendar is precisely the same as the Dionysian in a Greek form . 
This is shown by Tables B and C. (89, 90.) And the Council of Nicea decided 
that Jerusalem should be the prime meridian, when it decided that Easter should 
not be held on the 14th Nisan, since this is a Hebrew date, and that counts Jeru- 
salem as the prime meridian. And it is the prime meridian of all Hebrew and 
Christian calendars. (1-11, 85, 89.) 

(11 7). Contra. Fifth. Dr. Hill continues : " The Nicean Council, says the Abbe 
Guettee, ordered that the Christian Easter should be kept always after the Jewish 
Passover, as the substance after the type. By the Latin and Anglican rules, this 
law is sometimes violated." 

(11§) Now. By the Nicean rule, Easter always falls on the Mosaic date of the 
Passover, when that falls on Sunday, since the day to be avoided is the day before 
the Passover, as the anniversary of the Crucifixion. AC. 1st and 2d Examples show 
that in 1823 and 1903 Easter and the Passover fall on the same day. But in both 
cases it is the day of full moon. By the Mosaic rule the 14th day of Nisan was 
the day of full moon. And the full moon could not possibly fall later than the 
end of the 14th. So that NS. Easter fell on the forbidden 14th Nisan, and the 
Hebrews held the Passover on the Mosaic 14th Nisan. AC. Indexes put Easter one 
week later, and HCM. Rule 1 puts the Passover one day later. (1-11, 72, 73.) 

(119). Contra. Sixth. Dr. Hill continues : " The Greeks may admit the Grego- 
rian Calendar, but never the Latin rule of Easter. The ordinance of the Council 
must be held superior to mere scientific adjustment." 

Now. This appears to signify that the Greeks may admit the Gregorian Calendar 
as to civil dates, but never change their present rule to find Easter, since they 
regard that as the ordinance of the Council of Nicea. But it is above shown that 
the Dionysian Cycle never gave correct dates. It began AD. 534 with omitting 
one of the moons of Nisan, and including one moon of Zif. Now it has five 
moons of Zif to the exclusion of five moons of Nisan. It began with dates two 
days before full moon, and this frequently brought Easter on the forbidden 14th 
Nisan. And these original errors arose from misunderstanding the Alexandrian 
Canon, which is a " scientific adjustment " to give lunar dates. And even this was 
not by ordinance of the Council as Jarvis says (pp. 87-92), for Delambre, Long, 
Neale, Seabury, Brady, say that no such Canons are found among the proceedings 
of the Council. And from internal evidence it appears to have been the Egyptian 
substitute for a modern almanac. This we know was the use of a similar Egyptian 
cycle in the Julian Calendar. (JE. Table.) (94-98, 102-104.) 

Table A. Epacts (81). 

(120). In the Roman mode of determining ecclesiastical dates by NS. Table 
VII., the Dominical and the Epact are given. The Missal gives a table for 3G5 
days in the year, with the Roman and the modern day of the month, and the Sun- 

31 



AC. NOTES. 

day letter and the epact for each day of the month. The GN. are not given, but 
when this Table of Epacts is collated with the Alexandrian Cycle, and with the 
cycle in the Julian Calendar (in JE. Table) it is seen that each GN. 3 of the former 
and GN. 1 of the latter is marked with an asterisk as the fundamental epact at 
Jan. 1, 31, 60, 90, 119, 149, 178, 208, 237, 267, 296, 336, 355. This shows a regu- 
lar alternation of 30 and 29 days. And these asterisks are shown at March 1 and 
31 in the Table A as copied from the Missal. And the NS. Retractions are pro- 
duced by the double Epacts at April 4 and 5 in the table for new moons, as by 
retracting the dates of GN. from April 19 and 18 in the Anglican mode, in IS5TS. 
Table III. (66-70, 84.) 

(121). In AC. Table I. the Epacts are 13 days later than in the Roman Missal, 
and the double Epacts 25 and 24 are omitted in omitting the NS. Retractions by 
Contra. Rule 8. These Epacts and the Sunday letters are permanently attached 
to the same dates. In the Anglican mode the dates of the GN. are given in AC. 
Table IV. as they here stand with the corresponding Sunday letters. Then the 
Dominical will show which is the next Sunday after the date of that GN. In the 
Roman mode, the Epact is given. This is substantially the date of the GK, and 
AC. Rule 5 is substantially the same as AC. Rule 4. And for each day advance 
of the date of the GN., the Epact will recede one day, as shown in AC. Table I. 
(29, 30, 61-63, 66-70, 100, 101.) 

(122). Contra. First. The Rev. Samuel Seabury, D.D., on "The Theory and 
Use of the Church Calendar" (p. xii.), explains for the use of "laymen" (p. xi.) 
"a traditionary system which disclaims demonstration." And (p. 7), "Neither 
is it necessary for one to be either an astronomer or a mathematician." And (p. 
117), " Science must come down from her throne and condescend to accept the 
cycles which the custodians of the Church have treasured up." And (p. 118), " It 
must be kept wholly out of the domain of demonstrative science." And (p. x.), 
"I know of no treatise specially devoted to it." And (p. xi.), "A rule which 
may indeed be verified by experiment, but the reason for which no author that I 
have seen has been at the pains to unfold." 

(128). Now. The Council of Nicea in AD. 325 decided that Easter should not 
fall on the 14th day of Msan, the anniversary of the Crucifixion, but on the Sun- 
day next thereafter. Different artificial calendars have been constructed to give 
this astronomic date. It is purely a question for science to determine whether their 
authors have succeeded in doing what they attempted to do. Its importance is a 
matter of opinion. Science deals only with facts. (1-11, 40, 48-51, 54, 93, 102- 
108, 124.) 

(124). Contra. Second. Dr. Seabury (p. xiv.) desires to "recast" the Anglican 
Calendar and use epacts instead of golden numbers. He calls golden numbers 
"the peculiarities of the Hanoverian method, which has been fastened upon us in 
our English and American Prayer Books" (pp. 123, 194 ; xiv. ; 89 ; 189 ; 200 ; 211). 
Then (pp. 193, 194), "As if the Church, wearied of God's own ordinance for the 
regulation of her ancient solemnities, should choose some strange light, which 
should shine like the Dog Star but for one month in the year. ... In no other age 
. . . . could the heirloom of a thousand years be torn from her without a protest." 
Then (pp. 197, 198, 211), "Why direct us to Easter by Golden Numbers, with 
complicated tables for changing them century after century, instead of directing ua 
to find Easter by means of the simple and immutable system of epacts." And (p. 

32 



AC. NOTES. 

206\ " That wilderness of figures which constitute the Second and Third of our 
General Tables." 

(125). Now. First. The Dog Star is visible to the naked eye for about eleven 
months, and becomes invisible in the light of the sun for about one month. Sec- 
ond. What he means by " God's own ordinance " is not obvious. He may mean the 
epacts, since the Missal gives ttiem for every day in the year. But those are mod- 
ern, and were not used "for the regulation of her ancient solemnities." He may 
ineau the first Christian Calendar (NC), since that gave the date of every new moon. 
And that was used "for the regulation of her ancient solemnities." But that ap- 
pears to have been the Egyptian substitute for a modern almanac. And that was 
not used to determine the date of Easter until the century after the Council of 
Nicea in AD. 325. (94-101, 119-121.) 

(126). Third. "The heirloom of a thousand years" (AD. 534 to 1582) was the 
Dionysian Cycle (OS.). This, like the present Anglican tables, gave only the full 
moons of Nisan in one month, and therefore shone "but for one month in the 
year. " And when the Church of Rome introduced epacts for the whole year, the 
Anglicans retained the form of this "heirloom." And the Greeks still retain it in- 
tact. (83-85, 88, 92.) 

(127). Fourth. "The Hanoverian method" of giving lunar dates by Golden 
Numbers in a cycle of 19 j^ears was used by Meton, BC. 432 (OE.) and in the Jul- 
ian Calendar of BC. 45 ( JE.), and in the first Christian Calendar of about AD. 425 
(JE. Table), and in the Dionysian Cycle of AD. 534 (OS.). And this remained "the 
heirloom of a thousand years " until in AD. 1582 the Church of Rome substituted 
epacts. And the Greek Church still uses the Dionysian cycle with Greek Golden 
Numbers (AM.). And the Hebrews use GN. (HC). (81-93.) 

(128). Fifth. The Golden Numbers are not found in the Missal in connection 
with the epacts, except in explanatory tables. But when the two Egyptian cycles 
are collated with the epacts (JE. Table) the epacts are found to make the standard 
— every GN. 3 of one, and every GN. 1 of the other. And these "permanent and 
immutable " epacts are like Sunday letters, and the epacts found by rule are like 
the Dominical, to determine which of the permanent epacts is to be used. And 
epacts are substantially dates of the GN. in the reverse order. And the Church of 
Rome changes its epacts "century after century," to produce the same effect 
as ' ' that wilderness of figures which constitute the Second and Third of our 
General Tables." And the Anglicans had 170 years to simplify the rules from 
AD. 1582, when NS. began, to 1752, when it was adopted (entire) by England. 
And that "wilderness of figures" (NS., Table III.) is a splendid specimen of con- 
densation, and so simple that the whole 570 dates can with ease be memorized 
And the entire NS. system is contained in NS. Tables II. and III. On the con- 
trary, the Roman Missal takes two tables and 52 lines of printing to explain only 
one change of epacts, and then refers to a nameless "book" for further informa- 
tion as to the remaining 28 changes during the time covered by NS. Table II. (29, 
30, 61-63, 120, 121.) 

(129). Contra. Third. Dr. Seabury(pp. 78, 67, 71, 72, 90), " The Alexandrian 
Canon was founded on the lunar cycle of Meton (reduced from 6940 to 6939 days 
18 hours." And (p. 19), " The Hebrews .... in common with most ancient 
nations .... began the civil year which was a solar year of 365 days, at the au- 
tumnal equinox." And (p. 14), "365 days are still assumed to be the length of the 

33 



AC. NOTES. 

year in the Calendar of the Church and of all civilized nations." And (p. 225), 
" Ten days which were cancelled in 1582 on account of the precession of the equi- 
noxes." 

(130). Now. First. The Egyptian (NC.) and the Metonic (OE.) and the Hebrew 
(HC.) cycles all contain 19 years, because 235 lunations are nearly the same as 19 
years. But neither is founded on the other. They are all fundamentally different. 
Second. The ancient Hebrews counted from the vernal equinox (HCM.). Their 
years consisted of 12 or 13 lunations, and had about as many lengths as the present 
Hebrew Calendar (HC.) which makes the years 353, 354, 355, S83, 384, 385, but 
never 365. And the Metonic cycle (OE.) counted from the summer solstice, and 
like the Hebrews, their years were lunar. The Romans began the year on Jan. 1, 
and had 1461 days in 4 years, or 365.25 on the average. And no known calendar 
had consecutive years of 365 days except the ancient Egyptian (NE.), and that had 
no regard for equinoxes or solstices. Third. The precession of the equinoxes has 
no effect upon calendar dates. It would be unknown if there were no fixed stars. 
(101.) 

(131). Before the introduction of the Gregorian Calendar, Peter ab Alliaco and 
Cusa had proposed a reformation of the calendar to the Councils of Constance and 
of Lateran. In 1474 Sextus IV. engaged Regiomontanus (Muler), who died, and the 
work was stopped. Gregory XIII. acted under the advice of Clavius and Ciaco- 
nius, Aloysius, Lilius, and others. This Council of astronomers used the Alphon- 
sine Tables of the sun, and Tycho Brahe's of the moon, and were ten years in 
framing the calendar. And Delambre (Vol. 1, p. 12) says : "I found it better than 
its authors supposed it to be." (Long, Sec. 1244-1273 ; Jarvis, pp. 95, 96, 105-110 ; 
Brady, pp. 28, 29 ; Adams, pp. 354, 355 ; Wheatly, pp. 34-47 ; Renwick— Calen- 
dar ; Rees — Calendar, Cycle, Number ; Missal — De festibus mobilibus ; Mouravieff, 
Vol. 1, pp. 355-6 ; Delambre, Vol. 1, p. 12). Long (1267) says that Clavius explains 
the system and defends it from the attacks of Msestrinus, Vieta, and Scaliger. 

(132). Authors. 

Adams' Roman Antiquities. 
Alphonsine Tables. 

Barnard, pp. 538-589, Journal of Gen. Con. P.E.C. in 1871. 
Blunt, Annotated Prayer Book. 
Brady, John, Clavis Calandria. 

C.P. refers to the Anglican Common Prayer Book preface. 
Delambre, Histoire de l'Astronomie Moderne 

De Morgan, Book of Almanacs, and rules of the Gregorian Calendar in G.N. 
Almanac of 1846. 
Dodwell, De Veteribus Graecorum, Romanorumque Cyclis. 
Hartt, Joseph, Medulla Conciliarum. 
Home's Introduction. 
Jackson's Chronological Antiquities. 
Jahn's Biblical Archaeology. 
Jarvis' Chronological History of the Church. 
Long's Astronomy. 
Missale Romanum. 

34 



AC. NOTES. 

JVfontucla, Histoire des Mathematiques. 

Mouravieff, History of the Church of Russia. 

Neale, Feasts and Fasts. History of the Holy Eastern Church. 

Newton's Chronology. 

Prayer Book, Anglican, Preface. 

Rees' Cyclopedia. 

Renwick's Outlines. 

Scaliger, De Emendatione Temporum. 

Schaff s Bible Dictionary. 

Seabury, Theory and Use of the Church Calendar. 

Smith's Dictionary of the Bible. 

Smyth's Celestial Cycle. 

Tycho Brahe, Astronomies Progymnasmata. 

Wheatly, on the Book of Common Prayer. 

For Hebrew authorities see HC. Notes. 

Fulton, John, Index Canonum. 



35 



AE. 



AE=Actian Era = Augustan Era=new Egyptian Era, began NE. 720, Thoth 
lst= JP. 4685 Aug. 30 regular, but called Aug. 29 by the Romans. 

AE. Bule 1. For the year JP., add 4684 to the beginning of the year AE. And 
for the beginning of the year AE., subtract 4684 from the year JP. 

AE. Rule 2. For the year JC, subtract one from the year JP. or AE., and divide 
R by 4, and 2d R=year JC 

AE. Bule 3. For the day of Thoth. Add the given day of the given month to 
the number prefixed to that month in the following table : 4- Thoth ; 30+Paopi ; 
60-j-Athir; 90+Choiak; 120+Tybi ; 150+Meheir ; 180+Phamenoth ; 210+Phar- 
mouthi ; 240+Pachon ; 270+Payni ; 300+Epiphi ; 330+Mesori ; 360+Epago- 
menai. 

AE. Bule 4. For the day of the month. Subtract from the day of Thoth the 
number which is next less in Rule 3, and R=the day of the month to which that 
number is prefixed. 

AE. Bule 5. For AE. OS. into JP. (changing only the number of the year NE.) : 
Multiply the year AE. by 365, and to P add the day of Thoth (by rule 3) and the 
constant 1,710,707, and S=DJP. 

AE. Bule 6. For JP. into AE. OS. Reduce the date to DJP. (A). From DJP. 
subtract 1,710,707. Divide R by 365 for Q = year AE., and 2d R = day of 
Thoth, which reduce by rule 4. 

AE. Bule 7. AE. NS. into JP. (changing the number of the year KE. and add- 
ing a sixth Epagomenas in the same year as the Roman Bissextile). Subtract 
one from the year AE. Divide R by 4 for 1st Q and 2d R. Multiply 1st Q by 1461 
and 2d R by 365. To the two products add the day of Thoth (rule 3) and the con- 
stant 1,711,071, and S=DJP. (A). 

AE. Bule 8. JP. into AE. NS. From DJP. subtract 1,711,071. Divide 1st 
R by 1461 for 1st Q and 2d R. Divide 2d R by 365 for 2d Q and 3d R=day of 
Thoth. Multiply 1st Q by 4, and to L J add the 2d Q and the constant one, and S 
=year AE. Then reduce the day of Thoth by rule 4. 

AE. Bule 9. For JE. Correction. If the year AE. or JP. 
be found in this table, then for the actual Roman date, 
subtract from the regular date found by AE. Rules 5 or 
7 the number of days in the third column from Feb. 25 
+days opposite to the year, until Feb. 25+ days oppo- 
site to the next year in the table. And to find the regular 
date for rules AC. Rules 6 and 8 from the actual Roman 
dates, add the days in this table from Feb. 25 of the year 
opposite, to Feb. 25 of the next year in the table. 



AE. 


JP. 


Day. 


1 


4685 


1 


3 


4687 


2 


5 


4689 


1 


6 


4690 


2 


12 


4696 


3 


13 


4697 


2 


15 


4699 


3 


17 


4701 


2 


18 


4702 


3 


21 


4705 


2 


25 


4709 


1 


29 


4713 





33 


4717 






AE. 

AE. 1st Ex. For AE. OS.— On the authority of Censorinus, AE. began JP. 
4685=NE. 720. By the Rules of NE., Thoth 1st fell on Aug. 30 in NE. 720. 
Then by AE. Rule 5 ; AE. lx365+Thoth 1+constant 1,710, 707=DJP. 1,710,073. 
Then DJP. 1,710,073-365; -*-1461=Q 1170+R1338; -365=2d Q 3+2d R= 
Jan. 240, which in JC. 0=Aug. 30. Then Q 1170x4+2d Q 3+2=JP. 4685. 

Thus for all time AE. OS. will give the same day of the month as the ancient 
NE., but differ only in the year. And all the rules give the regular dates, without 
regard to the JE. Correction by Rule 9. For the year JP. 4685, subtract one day 
from Aug. 30, leaves Aug. 29 the actual Roman date of 1st Thoth. 

AE. 2d Ex. For AE. NS. AE. 5, Thoth 1. Then AE. 5-1 ;-s-4=Q 1+R ; 
Q 1X1461 +R 0x365+Thoth 1+constant 1,711,071=DJP. 1,712,533=JP. 4.689 
Jan. 242 in JC. 0=Aug. 29. By Rule 9 subtract one day=Aug. 28 the actual Ro 
man date, and required an extra intercalary to make Thoth 1st, the same as the Ro- 
man Aug. 29, at its erroneous date. 

AE. M Ex. For AE. NS. AE. 33. Thoth 1=DJP. 1,722,760=JP. 4717, 
Jan. 242 in JC. 0=Aug. 29, regular date and the Roman date, requiring the inter- 
calary in the same regular year as the Roman year, to keep Thoth 1st always the 
same day as the regular Roman Aug. 29. 

AE. teli Ex. For AE. OS. Censorinus says that in AE. 267, Thoth 1st fell on 
June 25. Then 267x365+1+1, 710, 707=DJP. 1,808,163=JP. 4951 June 25. This 
shows that AE. NS. was not in general use. 

AE. 5th Ex. For AE. NS. Josephus published his Antiquities in AE. 122, and 
synchronizes Pharmouthi with the Macedonian Xanthicus, or April. Now, by 
AE. Rule 3, Pharmouthi lst=Thoth 211. Then AE. 122, Thoth 211=DJP. 
1,755,477=JP. 4807, Jan. 86 in JC. 2=March 27=lst Pharmouthi. So that April 
began on 6th Pharmouthi. This proves that Josephus used AE. NS., for by AE. 
OS., the 1st Pharmouthi fell AE. 122, Feb. 26. (HC. Notes 91, 111, 113.) 



AE. NOTES. 



1. AE— Augustan Era=Actian Era = new Egyptian Era ; founded on the vie 
tory of Augustus over Antony and Cleopatra, at the naval battle near the promon- 
tory of Actium. 

2. Rule 1 makes AE. 1=JP. 4685, on the authority of Censorinus, "that most 
excellent and most learned vindicator of dates and of antiquity " (Scaliger, p. 201). 
And (p. 236) Scaliger says that " Censorinus states, that the Augustan Actian year 

267 was 986 of Nabonassar." And Jarvis (p. 118) says of Censorinus, that "in 

the year in which he wrote (the 283d of Csesar's Eef ormed Calendar and as he com- 
putes the 267th of the Egyptian Augustan years) the first of Thoth fell on June 
25th." (AE., 4th Ex.) 

3. Now : AE. 267 from NE. 986 leaves 719 years difference, so that AE. 1+719 
=NE. 720. But Scaliger (p. 236) says this makes AE. 1=NE. 719. Then JE. 
283+4668= JP. 4951, subtract 267 leaves 4684 difference, so that AE. 1+4684= 
JP. 4685. 

4. Contra. Scaliger as above, makes AE. 1=NE. 719. And (Prol. xxii.) he 
says, that JE. 43=AE. 28, or a difference of 15, so that AE. 1+15=JE. 16: 
JP. 4684. And the Oxford Chronological Tables give AE. 1=JP. 4687. (9.) 

5. Rules 5, 6. For the constant 1,710,707. AE. 1=NE. 720. Then NE. 720, 
Thoth 1=DJP. 1,711,073= AE. 1, Thoth 1. Then to leave room for AE. 1x365 ; 
+Thoth 1, subtract 366 from 1,711,073 leaves the constant 1,710,707. 

6. Rules 7, 8. For the constant 1,711,071. Assume that the change from AE. 
OS. to AE. NS. was made in AE. 1=JP. 4685= JC. 0, by inserting in that year 
the sixth epagomenas, so as to add one day in the same year as the Roman bissex- 
tile and make Thoth 1st the same as Aug. 29 or Jan. 242 in JC. 0. Then to put 
this extra day in AE. 1, 5, 9, etc., subtract one from the year AE., so that R 0, 4, 
8, etc.,-j-4 leaves 2d R=0, and QX1461 puts the extra day in AE. 1, 5, 9, etc. 
Then to make Thoth 1st fall JP. 4685 Jan. 242, this date=DJP. 1,711,072. Sub- 
tract one day to leave room for Thoth 1st and the constant =1,71 1,071. 

7. This does not imply that the change was made in AE. 1. It gives for all 
time the date of Thoth lst=Aug. 29, regular. In AE. 1=KE. 720, Thoth 1 fell 
on Aug. 30 regular, and in AE. 5, Thoth 1 fell on Aug. 29 regular. But the 
Romans counted both these dates one day less, so that in AE. 1, the regular 
Aug. 30 was the Roman Aug. 29, and without any change in AE. 1, this Roman 
date Aug. 29 was made permanent. Then in AE. 5, the Romans counted the reg- 
ular Aug. 29 as 28, and this required an extra day to make it the Roman Aug. 29. 
But AE. 5 was the regular bissextile, while the Roman bissextile w as AE. 3, so 
that AE. 3 or JP. 4687 must have been the first year in which AE. NS. used the 
sixth Epagomenas. (4, 9.) 

8. Rule 9 gives the difference between the regular dates of calculation and the 
actual Roman dates. Rules 7, 8 for AE. NS., follow all the irregularities of the 
Roman dates, by making Thoth 1st always fall on Aug. 29. These are the regular 
dates. But they have the same name as the Roman dates, and thus give Roman 
dates when corrected by Rule 9. But when dates are recorded, for comparison 
with other dates, by JP., this difference must be recognized. 

3 



AE. NOTES. 



9. The adjoining table will illustrate Rule 
9. The Julian Calendar (JE.) began with a 
bissextile JE. 1. The system required a bis- 
sextile every four years, as shown in column 
3. And all calculations assume that the bis- 
sextiles were observed as in column 3, and 
these make Aug. 29 fall at a uniform date as 
shown in column 5. Caesar was assassinated. 
Sosigenes, the author of the calendar, dis- 
appeared. The priests who had charge of 
the calendar, had a bissextile every " fourth " 
year as the Romans count, so that they fell 
as in the 4th column. And in JE. 34 the 
actual date Aug. 26 was the same day as the 
regular Aug. 29, as shown in columns 5, 6. 
To correct this error Augustus omitted the 
intercalaries in the three regular years JE. 
37, 41, 45, so that in JE. 45 (BC. 1) after the 
last omission of "Bis-sextum Kalendas Mar- 
tii," the dates became regular, and in JE. 
49 (the next regular year for the bissextile) 
the intercalation was resumed and carried 
on regularly. 



JE. COIIRECTIONS. 


1 


2 


3 


4 


5 


6 


7 


8 


9 










_S 


















"5 


^2 








Oh" 

u 

a 




02 . 

m E- 


CO 


bf. 

ea 

M 

oi 

be 

P 


5 5 
« o 

. a> 
buz 

o — 


< 


me 




*H 


>* 


cq 


5 


< 


» 


(H 


< 


< 


4669 


1 


1 


1 


29 


29 








4670 


2 








29 








1 


3 








29 








2 


4 




2 




28 








3 


5 


2 




29 


29 








4 


6 








29 








5 


7 




3 




28 








6 


8 








28 








7 


9 


3 




29 


29 








8 


10 




4 




28 








9 


11 








28 








4680 


12 








28 








1 


13 


4 


5 


29 


28 








2 


14 








28 








3 


15 








28 








4 


16 




6 




27 








5 


17 


5 




29 


28 


1 


30 


29 


6 


18 








28 








7 


19 




7 




27 








8 


20 








27 








9 


21 


6 




29 


28 


5 


29 


29 


4690 


22 




8 




27 








1 


23 








2? 








2 


24 








27 








3 


25 


7 


9 


29 


27 


9 


28 


29 


4 


26 








27 








5 


27 








27 








6 


28 




10 




26 








7 


29 


8 




29 


27 


13 


27 


29 


8 


30 








27 








9 


31 




11 




26 








4700 


32 








26 








1 


33 


9 




29 


27 


17 


26 


29 


2 


34 




12 




26 








3 


35 








26 








4 


36 








26 








5 


37 


10 




29 


27 


21 


25 


29 


6 


88 








27 








7 


39 








27 








8 


40 








27 








9 


41 


11 




29 


28 


25 


24 


29 


4710 


42 








28 








1 


43 








28 








2 


44 








28 








3 


45 


12 




29 


29 


29 


23 


29 


4 


46 








29 








5 


47 








29 








6 


48 








29 








4717 


49 


13 


13 


29 


29 


33 


22 


29 



AE. NOTES. 

10. Contra. Scaliger (p. 231) gives a table which shows the regular bissextiles 
the same as in column 3, but extended to JE. 53. Then the irregular bissextiles 
the same as in column 4, except that he omits the intercalation in JE. 1, and 
extends it to JE. 37, and makes the intercalations coincide in JE. 53 instead of JE 
49. That is, Scaliger agrees with columns 3, 4, which agree with Jarvis (p. 113) 
except that Scaliger supposes that Sosigenes did not carry out his own system by 
beginning with a bissextile. 

11. Again. Scaliger (p. 236) says : "At length in the Julian year 49, which 
was the twelfth running, of those which Augustus passed without intercalation, 
they counted the quarter of a day at the end of Aug. 28, and in the 52d year at 
the end of the same 28th day was intercalated one day composed of four quarters, 
which was the first correct (or regular recta) intercalation in the Actian Era." 
Now : That the year 49 was passed without intercalation, agrees with his contra- 
dictory statement above. But the year 52 was not a bissextile in either case. And 
the connection is not obvious, between the present question, and "a quarter of a 
day at the end of Aug. 28" in JE. 49, and "one day composed of four quarters 
.... intercalated at the end of the same 28th day " in the 52d year. Nor is it 
obvious what he means, by the statement that the intercalation of the day com- 
posed of four quarters at the end of Aug. 28 in JE. 52, "was the first correct (or 
regular) intercalation in the Actian Era." For if this signifies that in JE. 52 the 
Egyptians first made Thoth 1st, to coincide with the Roman Aug. 29, then the 
Egyptians must have interpolated seven days, since in JE. 52, Thoth 1st of the 
old year, had receded to Aug. 22, as shown in the table. If it signifies that the 
Egyptians had followed the irregular intercalation of the Romans (as supposed in 
AC. Rules 7, 8), and that the first regular intercalation was in JE. 52, then they 
made a "regular" intercalation, at an irregular date, since JE. 52 was not a regu- 
lar bissextile, according to Scaliger himself. 

12. Contra 2d. Jarvis (p. 117) says: "In AJP. 4689, the Roman system of insert- 
ing one day in every four years appears to have been adopted." Here he contra- 
dicts his own statement as shown in the table, for at that time the Romans inserted 
one day in every three years. He continues : " Because in that year the first day 
of Thoth coincided with that day," i. e., Aug. 29. Now, the table shows, that in 
JP. 4685, Thoth 1st fell on the regular Aug. 30, which by the Romans was counted 
Aug. 29. So that there was no necessity of inserting one day to make them agree. 
For the same reason there would have been no necessity of inserting one day in 
JP. 4689 to make them agree if " in that year the first day of Thoth coincided 
with that day." And the table shows that in JP. 4689, the first day of Thoth did 
fall on Aug. 29. But this was the regular Aug. 29 of calculation which the 
Romans called Aug. 28. So that an extra day was required in JP. 4689. But 
this was the year for the regular bissextile of calculation, while the actual Roman 
bissextile was JP. 4687 (as all agree), so that the first insertion of the extra day 
must have been in JP. 4687, two years after the beginning of AE. in JP. 4685 
according to Censorinus. And this may be what is intended by the Oxford Chron- 
ological Tables in making the Actian Era begin JP. 4687. (AC. Note 132 ; JE. 
Notes 7-17.) 



Al. 



Russo-Greek Calendar. 
AM = Anno Mundi = Year of the World* 

1. For the year AM. add 5508 to the year AD., or subtract the year BC. from 
5509. For the year AD. subtract 5508 from the year AM. For the year BC, sab 
tract the year AM. from 5509. 

2. CYCLES. Divide the year AM. by the Circle 19 for AM. GN. (Golden num- 
ber or lunar cycle) ; or by the Circle 28 for AM. Solar Cycle ; or by the Circle 15 for 
Iudiction ; and the remainder will be the year of the cycle. 



-a. 



3. HAGIOI\-PA§CHA= Greek Easter. Find AM. GN. and 
Solar Cycle (AM. 2). Then opposite to AM. GX., in the adjoining 
table, find the date of Nomikon Pascha, or ecclesiastical full moon. 
Then in (AM. 6) find the year of the Solar cycle at the head of one 
of the columns, and under that number, find the Ferial 1 to 7 = 
Sunday to Saturday for the 1, 8, 15, 22, 29 of each of the months 
in that year, beginning with March 1. Subtract this Ferial from 
2 or 9, and the remainder is the day of the month on which falls 
Sunday. Then add periods of 7 days to find Sunday next after 
the Nomikon Pascha, and that is the date of Hagion Pascha = 
Greek Easter = OS. Easter. (NB. Calendars 11, 12 ; NB. GND. 
13 ; OS. 2 ; 3—2 ; NB. scale 7.) 



5. MOVEABLE FEASTS; find from the date of Hagion-Pascha or Eas- 
ter by (NS. 6). 



Date. 


1 
GN. 


March 21 


13 


'■ 22 


2 


" 24 


101 


" 25 


18 1 


" 27 


7 


" 29 


15 i 


" 30 


4! 


April 1 


12 i 


2 


1 


4 


9 


5 


17 


" 7 6| 


9' 14 


" 10| 3 


" 12! 11 


" 131 19 


" 15 


8 


" 17 


16 


" 18 


5 



6. SOLAR CYCLE. 





1 


o 


3 


9 i 4 


5 


6 




7 


13 


8 


15 


10 


11 


17 




12 


19 


14 


20 


21 


16 


23 




18 


24 


25 


26 


27 


22 


28 


March 


6 


7 


1 


2 | 3 


4 


5 


April 


2 


3 


4 


5 


6 


7 


1 


May 


4 


5 


6 


7 


1 


2 


3 


June 


7 


1 


o 


3 


4 


5 


6 


Julv 


2 


3 


4 


5 


6 


7 


1 f 


August 


5 


6 


7 


1 


2 


3 


4 


September 


1 


2 


3 


4 


5 


6 


7 


October 


3 


4 


5 


6 


7 


1 


2 


November 


6 


7 


1 


2 


3 


4 


5 


December 


1 


2 


3 


4 


5 


6 


7 


January 


4 


5 


6 


7 


1 


2 


o 


February 


7 


1 


2 


3 


4 


5 


6 



7. Examples extracted from the 
" Full Christian Calendar by the 
Metropolitan of Kiev, printed at 
Kiev, 1842." 



A 


g' 










<H 


< 














« 




!-i 
















>* 




5 


14 


o 

CO 

28 


H. Pascha. 


1853 


7364 


14 


11 


April 15 


1857 


7365 


15 


12 


1 


" 7 


1858 


7366 


1 


13 


2 


March 23 


1864 


7372 


7 


19 


8 


April 19 


11865 


7373 


8 


1 


9 


" 4 


,1866 


7374 


9 


2 


10 


March 27 


1 1867 


7375 


10 


3 


11 


April 16 



* See NS. Preface. 



AM. NOTES. 



(1). AM.=Anno Mundi=Greek Year of the World =Russo-Greek Calendar. 
The manner in which this calendar can be made to represent the Mcean rule with- 
out changing its cycles, is shown in AC. Tables II., III. Its errors and contradic- 
tions are shown in AC. Example 4, and in AC. Notes 30-119. 

(2). AM. is the Oriental form, as OS. is the Western form of the Dionysian 
Cycle, which added 13 days to the correct dates of 19 new moons in the Egyptian 
Cycle of 235 new moons, about the time of the Council of Nicea. This in AD. 
534 was adopted by the Council of Chalcedon to give the dates of the 19 full 
moons of Msan, to find the dates of Easter on the Sundays next thereafter in 
accordance with the Mcean rule. OS. retained the Egyptian numbering of the 
years in the cycle, which produces the remarkable connection between the GN. 
and their dates (Scale). But AM. changed this numbering, for the supposed pur- 
pose of making it agree with the numbering of the years in the cycle which was 
then in use by the Greeks. And if 3 years in a circle of 19 be added to GN. AM., 
the table of Nomikon Pasclia in AM. will be identical with the table of the Full 
Moons of Nisan in OS. ; for the same absolute years. And the Solar Cycle of 
AM. Rule 6 necessarily gives the same dates for the same days of the week, as 
does the Solar Cycle in OS. And throughout the two calendars are substantially 
identical, so that the rules of OS. will produce precisely the same results as tho 
rules of AM. And both calendars are given in a condensed form, with references 
to the rules described in NS., which are the same for ISTS., AM., and OS. 

(3). The year AM. is called the year of the Constantinopolitan Period. It was 
used by the Russo-Greeks as a civil date until AD. 1725, when they adopted the 
Dionysian Period (AD. and BC). They still retain Julian dates (OS.), which the 
Westerns abandoned when they adopted ISTS. And in correspondence, both dates 
are given, as ISTS. began Oct. 5-15 AD. 1582. And the years of their cycles begin 
with March 1st, as shown in AM. Rules 3 and 6, and in their modern cycle of new 
moons. (AM. GND. in GND.) (Brady, pp. 51-2 ; Mouravieff, pp. 355-6.) 

(4). The year AM. is an artificial period, analogous to Scaliger's Julian Period 
(JP.) for the Western cycles, as shown in AM. Rule 2, and Examples, which have 
been extracted to show the connection between the years AM. and the first and last 
years of the three cycles. But this use of AM. is so little known among the 
Greeks, that the Greek author of the "Book of the Litany," takes three pages to 
give the rules to find the years of the three cycles, which are given in three lines 
in AM. Rule 2. And that rule is an original deduction from these three pages, 
and from the examples. (10, 15.) 

2 



AM. NOTES. 

(5). The example of AD. 1864 shows one of the five years in each cycle of 19 
years, in which the Greek Easter falls a lunar month too late for the Nicean rule. 
(AC. Notes 85-91 ; 108-119.) 

(6). The year of Induction is the same year AD. by AM. Rule 2, and OS. Rule 
2, and NS. Rule 9. It was a general ecclesiastical date, when civil dates differed. 
In our almanacs it is each year given as the year of the "Roman Indiction." But 
it is Greek, as well as Roman. It began AD. 313. 

(7). The Solar Cycle in the original had letters instead of figures for the days of 
the week, which are numbered from the First to the Fifth, then Friday is called 
Paraskeue^ Preparation, and Saturday is Sabbaton. (HC. Note 78.) 

(8). The Examples in 6 columns are extracts from a table with 21 columns, in- 
cluding the columns of Lunar Bases (or Epacts) and Nomikon Pascha (or GN.) as 
given below. Then add the column of dates of New Moon for the corresponding 
GN. from a manuscript table of the 235 new moons in the cycle of 19 years, of 
which an extract is given in columns 2 and 7 of GND., with this rule in the orig- 
inal : "If you seek in the month of January or February, then it is necessary that 
you take the cycle of the moon [GN.] of the previous year." (3.) 



AJ). 


AM. 


Ind. 


S. Cy. 


L. Cy. 


L. B. 


H. Pas. 


N. Pas. 


N. Moon. 


1856 


7364 


xiv 


xxviii 


xi 


4 


April 15 


April 12 


Mar. 25 


1857 


7365 


XV 


I 


XII 


15 


April 7 


April 1 


April 13 


1858 


7866 


I 


II 


xm 


26 


Mar. 23 


Mar. 21 


April 2 


1864 


7372 


Vll 


Vlll 


XIX 


3 


April 19 


April 13 


Mar. 27 


1865 


7373 


Vlll 


IX 


I 


14 


April 4 


April 2 


April 14 


1866 


7374 


IX 


X 


II 


25 


Mar. 27 


Mar. 22 


April 3 


1867 


7375 


X 


XI 


III 


6 


April 16 


April 10 


Mar. 23 



(10). These examples show, Rule 1. For the year AM. add 5508 to the year 
AD. And Rule 2. For the three chronological cycles divide the year AM. by the 
circles 15, 28, and 19, and R=Indiction, Solar Cycle, Lunar Cycle (GN.). And 
the first and last years of each cycle are given. (3, 4.) 

(11). The Lunar Base of the Greeks is called the Epact by the Westerns, as 
proved by this column, thus : For NS. Epact, multiply GN. by 11, and to P add 
the key Epact and divide S by 30, and R=NS. Epact. Then modify this rule to 
meet 3 days' difference in dates, and the difference in numbering the years in the 
cycle which makes the last three years of the Greek cycle overlap the first three 
years of the Western cycle, and the rule becomes this : Multiply GN. by 11, and 
divide P by 30, and add 3 for AM. epact, except for the years GN. 17, 18, 19 add 
4 days, and if the sum exceed 30, then subtract 30, because the epact cannot be 
more than 30. (NS. 12 ; AC. Table 3, AC. Notes 29, 30, 61-63, 81-182.)- 

(12). The Greek lunar base necessarily remains the same for all time, since the 
epact is substantially the date of GN. in the reverse order, and the Greek dates of 
GN. remain the same for all time. And it is not required to determine ecclesiasti- 
cal dates. But NS. epacts are used by the Church of Rome to determine eccle- 
siastical dates, and they are changed century after century, to produce precisely the 

3 



AM. NOTES. 

same results, as by the Anglican mode of changing the dates of the GN. thirty times 
in a great lunar cycle in accordance with NS. Table II. (NS. 2, 7 ; NS. Notes 31-35.) 

(IS). In this extract, the dates of the Nomikon Pascha agree with Rule 4, which 
is copied from a manuscript table, except in accordance with this table by the 
Metropolitan, GN. 12 is dated April 1, while in the manuscript GN. 12 is dated 
March 31. This is certainly a mistake in copying. The addition of 3 years in a 
circle of 19, to the GN. in Rule 4, makes that table identical with the OS. Table, 
and the OS. Table is the original Dionysian cycle. (AC. Notes 81-132.) 

(14). The difficulty in finding the rules of this Russo-Greek Calendar (which at 
the present time governs the ecclesiastical dates of such a large section of the 
Christian Church) is very remarkable. The Western forms of the Christian Calen- 
dars, ancient and modern (OS. and NS.), are given in the ancient and modern 
Anglican Prayer Books and Roman Missals. And many authorities were found 
on these subjects. (AC. Note 132.) 

(15). But, while finding the Greek Calendar — of the saints, and several references 
to dates, I could not find the calendar of dates in any book, in Greek, Latin, 
French, German, or English, of which the title promised success, in private libra- 
ries and in the Astor Library. Then by advice of the Librarian, I called on Dr. 
Young (subsequently Bishop of Florida), as having the best Oriental library in the 
country. We could not find this calendar in the voluminous Greek service books, 
nor in the large book of Rubrics. Nor did he inform me where I could find it. 

(16). It was finally obtained in the "Full Christian Calendar, by the Metropoli- 
tan of Kiev," in Sclavonic text with Arabic mimerals, and in three leaves of the 
"Book of the Litany" in printed Greek, with a manuscript mediaeval Greek trans- 
lation of the Sclavonic, from "Father Agapius," who was a priest in the Russo- 
Greek Church, and a Sclavonian, and at that time the proof-reader of Sclavonic for 
the Bible Society. (4.) 

(17). Hence, no printed authority except the above, can be given for the rules 
of AM., while many are given for the rules of OS. and NS. This calendar can 
probably be found in the libraries of Theological Institutions, and certainly in 
Greece. It may differ in form as indicated in AC. Note 112. But it will doubt- 
less be substantially the same, since the "Metropolitan of Kiev " must be regarded 
as the highest authority. And the fact that AM., as he states it, is identical with 
OS., is strong evidence that his statements are correct. 

(1§). The rule " To find the Hagion Pascha," copied by photo-engraving, is ap- 
pended. This differs from ordinary print, about as much as our manuscript dif- 
fers from print. And Scaliger uses so many contractions in his Greek, that it dif- 
fers quite as much from ordinary print. And he introduces without translation, 
sentences in Greek, Hebrew, Arabic, etc., as parts of his Latin text. And his 
woik printed in 1629, was not very long after the time that a Greek sentence was 
omitted by the Latins, with the note : '• Grsecum est, non legitur " — " It is Greek, 
it is not read." 



ft*£* 



•s 



IS 



r 2 |. #'*■ 





44 









s 1 s^. 



,a 



6 If I-- 






*^fjifc 




& 



^ 1 

§4 ^\ 






i 









J- 



h'rfe I 






"§H S ^ I r ^ 










AU. 



AU=AUC=Anno Urbis Conditse=Year of the City Constructed = old Roman 
year. 

A TJ. Rule 1. For the year JP., add 3960 to the year AU. 

1. The early Roman dates are so uncertain that rules for positive dates within 
the year cannot be constructed. Romulus began his year in JP. 3961 with March. 
Then followed April, May, June, then Quintilis which was changed by Julius 
Csesar to July. Then Sextilis, which was changed by Augustus to August, then 
as we have them at the present time, Sept., Oct., Nov., Dec. All except the first 
four months, from Quintilis (fifth) to December (tenth), being numbered from 
March as the first. It is a disputed point whether January and February made up 
the 12 months, or whether the year of Romulus contained only 10 months. Jarvis 
(pp. 55-65) recites authorities to prove that it contained 12 months. And he sup- 
poses that the date had receded about 10 days, when in AU. 39 Numa modified the 
calendar of Romulus, confessedly on a Greek basis, and made January the first, 
the beginning of the year. 

2. Adams' Roman Antiquities (pp. 353, 355) says: "Numa in imitation of 
the Greeks divided the year into 12 months according to the course of the moon 
consisting of 354 days : he added one day more (Plin. 34.7) to make the number 

odd The Romans divided their months into three parts by Kalends, Nones, 

and Ides. The first day was called Kalendce vel Calendoe (a calendo vel vocando) 

from a priest calling out to the people that it was new moon the 13th Idus 

the Ides from the obsolete verb iduare, to divide, because the Ides divided the 
month." 

3. Now : In the absence of positive knowledge, we may infer that "the obsolete 
verb iduare" has been invented to agree with the fact that "the Ides divided the 
month." These names Kalends and Ides, with the facts that Numa divided the 
year into 12 lunar months, and changed the beginning of the year from 1st March 
to 1st January, indicate that Romulus adopted the calendar of a Greek colony, 
which counted 12 actual lunations in the year, as the Turks do at present (ME.). 
"We know that the Greeks so understood the oracle, that the first day of the month 
must be the day of the actual new moon (OE.). The classic Greeks called this 
Noumenia or new moon. The Romans called it Kalendoe, which is certainly from 
the Greek Kaleo, to call out or proclaim. Kalendoe being from the Greek, we may 
infer that Idus is from the Greek Eido (pronounced Ido) to see or observe. 

4. Now : it is an astronomic fact, that if at the Idus, an Observation (Eido) be 



* See NS. Preface. 



AIL 

taken to determine how many hours before or after midnight was the time of full 
moon, the number of days to the next new moon can be determined. Hence the 
inference that at the Idus the priest took an Observation (Eido) of the hour of full 
moon, and then proclaimed (Kaleo) how many days it would be to the next new 
moon, and the beginning of the month. And this Proclamation (Kaleo) made day 
after day, caused the Kalends to count backwards. In like manner the Greeks as 
far back as the time of Homer counted backwards from the beginning of the next 
month, but with this difference, the Greeks specified, that it was so many days be- 
fore the "Lost Moon" (OE.) The Romans simply called it a Proclamation (Kaleo) 
leaving the rest to be inferred. 

5. This supposes that the date was determined by actual observation analogous 
to the Mosaic rule among the Hebrews (HC). Then a year of 12 mean lunations 
would recede 10.875,148 days per year. This multiplied by 38 years from Romu- 
lus to Numa=413.25 days or one year and 48 days. If Numa postponed the change 
one year, then the 1st Jan. fell within one day of the same equinoxial date, as the 
1st March when established by Romulus, as the beginning of the year. 

6. Numa added one day to 354 (Plin. 34.7), says Adams (p. 353). This left about 
10 days intercalation to retain the same solar date. The Pontifex Maximus threw 
in these extra days according to his own judgment (arbitrio). These were inserted 
between Feb. 24 and Feb. 25. The one day intercalary in the bissextile of the Ju- 
lian Calendar (JE.) has the same position. The Church of Rome retains the same 
position. But others changed it to February 29 at the Savoy Conference in AD. 
1660. And it has been legally decided that thr: intercalary is a part of the previous 
day in counting ages. And since Feb. 24 is in Roman terms " Sextum Kalendas 
Martii" (JE.), this extra Feb. 24 is called "Bis-sextum Kalendas Martii," and the 
year in which it falls is a Bissextile, and thus differs from a Leap year with Feb. 
29 as the intercalary. 

7. These intercalaries were thrown into the calendar of Numa with such irregu- 
larity that no dependence can be placed upon Roman dates until AIL 707 Oct. 13. 
Sosigenes after framing JE., calculated the date backwards over the last " year of 
confusion." He divided 445 days into 15 months beginning Oct. 13 AU. 707, and 
ending Dec. 31 AU. 708, the day before Jan. 1 AU. 709. This is called the "Pro- 
leptic (or before taken) Julian year." But why it should have a Greek name is not 
obvious, since proleptic is Greek and not Latin. 

§. Thus, through more than 26 centuries the calendar of Romulus has sent down 
to us his names of the months except two of the numbered months, and all the 
numbered months counting from March, which was named after Mars the father of 
Romulus, who was deified as the God of War. (JE.) 



GNU. asail EPJLCTS. 

Notes respecting the following Cycles.* 



1 


2 


3 


i 
4 


5 1.6 | 7 | 8 


9 


10 


11 


12 


iS 


p 
Pi 

c3 




d 

O 

g 

<1 | 


3*: 


j 

g ! 

to ; 
o 

o ! 


s ! 

o 

o '< 
& i 


£ i £° 

O L, CO 

<! ! H 


CO 
u . 


c5jS 

DD O 


°£ ^ • 

1^ 02»G 
S| O 


jj 

o 

25 

Pa . 


67 


March. 8 


14 


16 


2 


2 


18^23 




23 








68 


9 


3 


5 




10 


7 22 




22 








69 


" 10 






10 




121 




21 








70 


" 11 


11 


13 




18 


15 20 




20 








71 


" 12 




2 


18 


7 


4:19 




19 








72 


•'. 13 


19 




7 


15 


18 




18 








73 


" 14 


8 


10 






12 17 




17 








74 


" 15 






15 




1 


16 




16 








75 


rt 18 


16 


18 


4 


4 




15 




15 








76 


" 17 


5 


7 




12 


9 


14 




14 








77 


" 18 






12 






13 




13 








78 


" 19 


13 


15 


1 


1 


17 


12 




12 








79 


" 20 


2 


4 






6 


11 




11 








80 


K 21 






9 


9 




10 


23 


10 


23 


18 


13 


81 


" 22 


10 


12 




17 


14 


9 


22 


9 


22 


5 


2 


82 


" 23 




1 


17 


6 


3 


8 


21 


8 


21 






83 


" '24 


18 




6 


14 




7 


20 


7 


23 


13 


10 


84 


" 25 


7 


9 






11 


6 


19 


6 


19 


2 


18 


85 


" 26 






14 






5 


18 


5 


18 






86 


" 27 


15 


17 


3 


3 


19 


4 


17 


4 


17 


10 


7 


87 


" 28 


4 


6 




11 


8 


3 


10 


3 


16 






88 


" 29 






11 






2 


15 


2 


15 


18 


15 


89 


" 30 


12 


14 




19 


16 


1 


14 


1 


14 


7 


4 


9Q 


" 31 


1 


3 


19 


8 


5 


•55- 


13 




13 






91 


April 1 


9 




8 


16 




29 


12 


29 


12 


15 


12 


92 


2 




11 


18 




13 


28 


11 


28 


11 


4 


1 


93 


3 


17 




5 


5 


2 


27 


10 


27 


10 






94 


" 4 


6 


19 








26(25) 


9 


23 


9 


12 


9 


95 


5 




8 


13 


13 


10 


25,24 


8 


25 


8 


1 


17 


98 


6 


14 


16 


2 


2 




23 


7 


24 


7 






97 


« 7 


3 


5 






18 


22 


6 


23, 22 


6 


9 


6 


98 


8 






10 


10 


7 


21 


5 


21 


5 






99 


9 


11 


13 




18 




20 


4 


20 


4 


17 


14 


109 


" 10 




2 


18 


7 


15 


19 


3 


19 


3 


6 


3 


101 


" 11 


19 




7 




4 


18 


2 


18 


2* 






102 


" 12 


8 


10 




15 




17 


1 


17 


1 


14 


11 


103 


" 13 






15 




12 


16 


X- 


16 


* 


3 


19 


104 


" 14 


16 


18 


4 


4 


1 


15 


29 


15 


29 






105 


" 15 


5 


7 








14 


28 


14 


28 


11 


8 


108 


" 16 






12 


12 


9 


13 


27 


13 


27 






107 


" 17 


13 


15 


1 






12 


28(25) 


12 


26 


19 


16 


108 


" 18 


2 


4 




1 


17 


11 


25,24 


11 


25 


8 


5 


109 


" 19 






9 


9 


6 


JO 




10 


24 




1 



Examples of different Golden Numbers and GN. Dates ; and corresponding 
JSpacts with explanations, numbe -ed as the columns. (AC. Note 106.) 

3. and 3d column. AU. NGN", were introduced with AU. or Julian Calendar at 
^* See NS. Preface. 1 



CJIVD. and EPACTS. 

the date of new moon BC. 45, Jan. 1, and have Jan. 1 ===== GN. 1 ; which makes the 
Basic year «= BC. 45, and AD. 325 == GN. 9. dated April 1. This is the first appear- 
ance of the Scale (NB. Scale). Contra. Jarvis (p. 95) supposes AD. 325 == AU. GN. 3. 

4. NC. NGN". (NB. NC.) has GN. 3 == March 31 and new moon fell AD. 325, 
March 31 (MDK.) This makes AD. 325 = GN. 3, and the Basic year = BC. 1, as at 
present, and for all intermediate Calendars except for (AM. GN.) Also, new moon 
in AD. 325 == April 1, by AU. GN. and March 31 by NC. GN., shows that NC. in 
modifying the Basic year of AU. GN. from BC. 45 to BC. l,also subtracted one day 
for the recession of the moon, which is one day in 308 Julian years. This is the lunar 
portion of NC. (NB. NC.) Contra. Jarvis (p. 95) says that new moon fell AD. 325, 
March 23, and hence AD. 325 =-= GN. 1. This discrepancy between AU. GN. and 
NC. GN., as stated by Jarvis, caused an investigation which formed the nucleus 
around which the whole of this work on Calendars and Almanacs has been crystal- 
lizing for the last ten years. Also, Jarvis (pp. 87-92) says that NC. GN. were " estab- 
lished by the Council of Nice." Contra. (NB. NC.) (AC. Note 54.) 

5. NGN. of CP. 1607, by taking the Basic year = BC. 1, shows 4 days recession 
from NC. NGN. (CP. 1607 == Common Prayer Book of 1607.) 

0. NGN. of CP. 1553 is very irregular, but taking the basic year = BC. 1 shows 
about 4 or 5 days recession from NC. NGN. (CP. of Edward VI. )f 

7. AM. NGN. have the basic year == AM. 1 (AM.), and make AD. 325 = AM. NGN. 
19. To convert AM. NGN. or AM. FGN. into the western GN. from JP.. add 3 or 
subtract 16 years. These then show a recession of 4 and 5 days from NC. NGN. 

8. (1.) Epacts for NS. NGN. in the Missal have * at each NC. NGN. 3, rep- 
resenting AD. 325. Then epacts in reverse order from 29 to 1 between * and *, with 
doubled epacts 25 (25) regular and extra in all spaces of 30 days from * to *, and 
doubled epacts 26 (25) regular and extra ; and 25, 24 regular in spaces of 29 
days (as seen at April 4, 5), and epacts 23, 19 doubled at Dec. 31, with the note. 
" This epact 19 is not to be used except in the year of the Golden number 19." 

(2.) Now any epact with its permanent date being assumed as the epact for any 
GN., will strike the same dates in the year as that GN. by Scale, including NS. Re- 
tractions. Hence by changing the epact for any GN. the date of that GN. is changed 
by the use of this " immutable system of epacts," and there is no necessity of 
changing the table in order to follow the moon as in (columns 5, 6, 7). Thus, during 
this century NS. Key epact = 19, and hence GN. 3 = epact 22 = April 7, in Epacts 
for NGND = 7 days later than GN. 3 = March 31 in NC. NGN ; or 5 days recession by 
NS. LG, and 12 days advance by NS. SC, making 7 days advance. The same 
change is produced by the NS. Index in the Anglican Table II. applied to NS. 
Table III. (NB. NS. 32). 

9. Epacts for NS. FGND. This is original. The dates are found by adding 13 
days to the Epacts for NGND. on or between March 8 and April 5 (== new moon of 
Nisan) to find FGND. of 14th Nisan. (NB. NS. 3 ; Table III.) 

10. Epacts for AC. NGN. shows the changes of (column 8) to meet (NB. AC. 
3,26). 

11. Epacts for AC. FGN. are found from (column 10) in the same manner as (col. 
9 from col. 8). 

12. OS. FGND. are found by adding 13 days to the dates of NC. NGN. to give 
the 14th Nisan in accordance with the compromise (NB. NC.) These were estab- 
lished by the Council of Chalcedon, AD. 534, " to find Easter for ever." (Wheatly, 
p. 38.) 

13. AM. FGN. Reduce AM. FGN. to JP. FGN. by adding 3 or subtracting 
16 years, and AM. FGND. becomes identical with OS. FGND. Hence AM. is 
only the Greek form of OS. 



t The first CP. of Edward VI. in AD. 1549, has GN. by scale from GN. 5 = March 8 
to GN. 4 = April 18. 2 



HC* 

HC.=HEBREW CALENDAR (MODERN). 
HCM.=HC. MOSAIC (ANCIENT). 



SUMMABY. 



The HC. Rules here given are more simple than elsewhere found. They are in 
precise accordance with the standard rules by Characters. The HC. Table of 
dates from AD. 1883 to AD. 1992, is substantially the same as given by Lindo in 
his " Jewish Calendar for 64 Years " They are required by the historian to deter- 
mine dates since AD. 1040, when this calendar was generally adopted. And its 
lunar dates are wonderfully accurate. But in the use of those dates there are 
several departures from the ancient rules. So that in determining ancient dates 
the historian requires the rules of HCM., with the following differences. 

1st. HC. makes Nisan begin before conjunction, and the Passover to fall on the 
same day as full moon or the day before full moon. These were impossible under 
the Mosaic rule. 

2d. HC. makes the Passovers fall on the day of the second full moon after the 
vernal equinox in each of the three years preceding GN. 1, 9, 12, since AD. 1630 
and GN. 4 will follow in AD. 1972. It thus makes the whole series of 19 Pass- 
overs advance a lunar month in 6501 years, and thus keep revolving through all 
seasons to the end of time. 

3d. HC. does not allow the Passovers to fall on Day ii, iv, vi. By the Mosaic 
rule there was no restriction. 

4th. HC. changes the number of days in Hesvan and in Kislev, to restrict the 
number of days in the year, to 353, 354, 355, 383, 384, 385. By the Mosaic rule 
there were no such changes. 

The HCM. Table of dates from AD. 1883 to AD. 1902, compared with the HC. 
Table of dates, will illustrate the present differences as to 1st and 2d, which are 
astronomic, while retaining the 3d and 4th, which are artificial. 

HCM. Example of the last sacrifices in the temple AD. 70, April 14, prove 
1st above. 

HC. and HCM. Examples from AD. 28 to AD. 34 illustrate the application of 
the rules of HCM. in determining which of the six years assigned by different 
authors was the actual year of the Crucifixion. 

Contradictions are numerous. The specific points are stated in the Table of 
Contents at the beginning of the notes. Then follow the Authors. 



* See NS. Preface. 



HC. 

HEBREW CALENDAR. 



HC. Rule 1. For the beginning of the year and day. Add 3761 to the year 
AD or subtract the year BC. from 3762. Or subtract 952 from the year JP. 
And for the year AD. subtract 3761 from the year HC; or for the year BC, sub- 
tract the year HC from 3762 ; or for the year JP. add 952 to the year HC — And 
this year EC. begins with the first day of Tisri, which begins in Hebrew time in 
the evening before noon of the day of the month and of the week as found by rule, 
in September or October. And this first day of Tisri determines all the Hebrew 
dates of the previous and of the current year, which fall in the same year AD., 
BC, or JP. And all count in Hebrew time from the evening before noon, of the 
day of the month and of the week as found by rule. 

HC. Rule 2. For the character of Moled Tisri: Divide the year HC, by the 
circle 19 for Q of past cycles, and R= GN. Then multiply separately the three 
terms of a cycle 2. .16. .595, by Q. And multiply the three terms of an embolis- 
mic year 5. .21. .589 by as many embolismic years as are before the given GN., 
counting GIST. 3, 6, 8, 11, 14, 17, 19 as embolismic. And multiply the three terms 
of a common year 4 . . 8 876 by as many common years as are before the given 
GN., counting as common years GN". 1, 2, 4, 5, 7, 9, 10, 12, 13, 15, 16, 18. Then 
to the sums of the multiples of these three terms, add the three terms of the stand- 
ard character 2 . . 5 . . 204, and reduce thus : 

Divide the sum of the third terms (scruples) by 1080 for Q of hours and R of 
scruples. Then add Q of hours to the sum of the second terms (hours), and divide 
this sum by 24 for Q of days, and R of hours. Then add this Q of days to the 
sum of the first terms (days) and divide by the circle 7, for R of days. And the 
R of days, and R of hours, and R of scruples, is the character of Moled Tisri, or the 
day of the week, and the hour, and the scruples, upon which falls the new moon 
of Tisri, counted in Hebrew time from six hours before midnight at Jerusalem. 

Or. Divide the year HC by the circle 19 for Q of past cycles and R=GN. 
Then multiply Q into the three terms of a cycle 2 . . 16 . . 595, and to these products add 
the three terms of the standard date 2 . . 5 . . 204. Then reduce these terms as above to 
find the character of GN. 1, of the current cycle. Then by HC. Rule 8 find by pro- 
gression, the character of Moled Tisri, for each of the 19 years in that c3 r cle. (BA.) 

HC. 1st Ex. AD. 1901+3761=HC. 5662 ;-- circle 19=Q 297+GN. 19. Then 
(2. .16. . 595) X 297 +(5. .21. .589) X 6 embolismic +(4. .8. .876) X 12 common+2. .5. . 
204 standard=674 days. .4979 hours. .190,965 scmples=vi. .19. .885= character of 
Moled Tisri AD. 1901 =GN. 19. 

HC. 2d Ex. Or (2. 16. .595)x297+2. .5. .204=596 .4757. .176,919=111. .0 . 
879 the character of Moled Tisri of GN. 1=AD. 1883. Then by Rule 8— as in 
HC Table AD. 1883 to 1902. 

HC. Rule 3. For the ferial of 1st Tisri : Make it the same as the ferial of 
Moled Tisri, except in the following cases, add as directed. 

J— Jach=18 hours. If the date be as much as 18 hours, then add one day for 
the date of 1st T'sri. 

B=Betuthakp7iat=II. .15. .589. If the character of a common year, next after 
an embolismic year be II. .15. .589 or more, then add one day. 

2 



HC. 



G=Getrad=III. .9. .204. If in any common year the character of the Moled be 
III. .9. .204 or more, then add two days. 

A=Adu=i, iv, vi. If in any case the 1st Tisri would fall on Day 1, iv, or vi, 
then add one day. 

JA= Jack and Adu combined, add two days. 

HO. Rule 4. For the lengths of years and months : In a circle of 7, subtract the 
ferial of the 1st Tisri of the given year, from the ferial of the 1st Tisri of the fol- 
lowing year, and let the remainder iii, iv, v in a common year be represented by 
s, o, 1 (short, ordinary, long) and the remainder in an embolismic year v, vi, vii= 
S, O, L, then will the number of days in the given year, and the days in the 
months in that year, be as follows : 













1 


2 


3 


4 


5 


6 




7 


8 


9' 


10 


11 


12 




Goxdhn 


c 


i ** 


a> 






























Numbers. 




T3 C 


JS 


















„_■ 
















O , 

o 5 


■5 a 

C3^ 


3 


1 




.a 


■5 




5 

q3 


a 

QQ 




a 

03 


n 


,a 


3 






A 
iii 


02 


Q 


30 


29 


29 


29 


02 

30 


< 
29 


l> 


30 


29 


02 

30 


Eh 
29 


< 
30 


m 




1, 2. 4, 5, 7, f 
9, 10, 12, 13 ,-{ 


353 


29 


IV 


O 


854 


30 


29 


30 


29 


30 


29 




30 


29 


30 


29 


30 


29 


oB»j 


15, 16, 18 (. 


V 


] 


355 


30 


30 


30 


29 


30 


29 




33 


29 


30 


29 


30 


29 


■ sO 


3, 6, 8, 11, r 

14, 17, 19 1 


V 


S 


383 


30 


29 


29 


29 


30 


30 


29 


30 


29 


30 


29 


30 


29 


Em 

1)0 

yeai 


VI 





384 


30 


29 


30 


29 


30 


30 


29 


30 


29 


30 


29 


30 


29 


vii 


L 


335 


30 


30 


30 


29 


30 


30 


29 


3J 


29 


30 


29 


30 


29 



HO. Rule 5. For Ecclesiastical Days : 1st Tisri=Rosh Ashana=]STew Year. 
10th Tisri=Kipur=Day of Expiation. 15th Tisri— Succot= Feast of Tabernacles. 
21st Tisri=Hosana Raba, i. e., Great=last day of the festival. 25th Kislev= 
Hanuca=Feast of Dedication. 14th Adar or Veadar=Purini. 1st JSTisan= ancient 
New Year, and present beginning of the ecclesiastical year. 15th Msan=first day 
of the Passover. 6th Sivan=Sebuot= Pentecost=Feast of Weeks. And these all 
begin in the evening before noon of the dates found by rule. 

HC. Rule 6. To simplify HC. Rule 2 (BA). For the year 
HC. add 3761 to the year AD. ; or subtract the year BC. from 
3762, or subtract 952 from the year JP. Then divide the year 
HC. by the circle 19 for Q of past cycles and R=GK Then 
multiply Q by 1565 and subtract the product from GND. of the 
given GN. for 2d R. Then subtract one from the year HC, 
and divide the remainder by 4, and multiply the new remainder 
by 6480 to find JCC, which add to 2d R. Divide this sum by 
25,920 for Q=day of August OS., and R=scruples. Divide the 
scruples by 1080 for Q=hours and R= scruples. Then if desired 
multiply the scruples by 3^, and divide the product by 60 for 
Q=minutes, and R=seconds. If the day of August OS., exceed 
31, then subtract 31 for R=day of September OS. If it exceed 
61, subtract 61 for R=day of October OS. If date NS. be de- 
sired then add NS. SC. (12 days from March 1, 1800, to March 1, 
1900, then 13 days to March 1, 2100, etc.) 



GN". 


GND. 


1 


1,768,164 


2 


1,486,080 


E 3 


1,203,996 


4 


1,687,345 


5 


1,405,261 


E 6 


1,123,177 


7 


1,606,526 


E 8 


1,324,442 


9 


1,807,791 


10 


1,525,707 


Ell 


1,243,623 


12 


1,726,972 


13 


1,444,888 


E14 


1,162,804 


15 


1,646,153 


16 


1,364,069 


E17 


1,081,985 


18 


1,565,334 


E19 


1,283,250 



HC. 

HG. Ex. AD. 1883+3761=HC. 5644;-^19=Q 297+GN. 1. Then 297x1565 
from l,768,164=2d R 1,303,359. Then HC. 5644-1 ;-4 leaves 8 ;X 6480=19440 
JCC;+1,303,359=1,322,799;-^25,920=Q 51 Aug. OS..+0 hours.. 879 scruples. 
Add 12 days NS. SC.=Date of Moled Tisri AD. 1883.. Oct. 2. .0 h..879 scr. 
(See HC. Table.) 

HC. Rule 7. For the ferial of Moled Tisri: Subtract one from the year HC, 
and divide R by 4 for Q and 2d R. Then multiply Q by 5, and to P, add 2d R, 
and the constant 4, and the day of August OS. (found by HC. Rule 6) and divide 
S by the circle 7, and R=the ferial. 

HC. Ex. AD. 1883=HC. 5644 ;-l=5643 ;^4=Q 1410+R 3. Then 1410x5+ 
3+4+51=7108 j-j-7 leaves ferial III. (See HC. Table.) 

HC. Rule 8. To tabulate .Dates.— Prepare a blank table similar to the table of ex- 
amples AD. 1883 to AD. 1902. At the heads of the columns put the following : 
Col. l = any year AD. Col. 5 = corresponding year HC. by rule 1, or 6. Col. 
7 = GN. found by rule 2, or 6. Col. 6 = day of the month, and Col. 8 = hours and 
scruples found by rule 6, and ferial found by rule 7, to complete the character of 
Moled Tisri in the corresponding year HC. Then prove this work in Col. 8, by 
finding the same character by rule 2. Then set down in consecutive order the years 
AD. HC. and GN., marking with L, the NS., Leap years (which AD. 1900 is not), 
and with E, the embolismic GN. as in rule 2 or 6. This completes the skel- 
eton. 

For Col. 8. E=v..21..589 and C=iv. .8. .876 ;= Character of an Embolismic 
(E), and of a Common (C) year. Then if the year of which the character has been 
found be E (or C) add the character v. .21. .589 (or iv. .8. .876), and reduce as in 
rule 2 to find the character of Moled Tisri of the next year. To prove the work, 
add ii. .16. .595 to the character of any GN. and reduce to find the result the same 
as the character of the same GN. in the next cycle. 

For Col. 9. By rule 3 find the proper symbols J, A, JA, B, G. 

For Col. 10. Add to the ferials in Col. 8 the number indicated in Col. 9. In all 
other cases mark the same ferial as in Col. 8. 

For Cols. 11, 12, fill out by rule 4. Then will Cols. 5, and 7 to 12, contain quan- 
tities which are exclusively Hebrew, without reference to any other calendar. And 
all the other dates can be found by rule 5. 

For date NS. in Cols. 6, 8, omitting the ferials. If the year for which the date 
has been found be E, then add 18 d. .21. .589 and reduce as above, except retain 
the sum of days (and it simplifies the work to call Oct. 2= Sept. 32). Then sub- 
tract one day if the next year be L, but nothing if it be not L. 

If GN. be not E, then add d. .8. .876 and reduce. Then subtract 12 days if the 
year AD. for which the new date is desired be L, or subtract 11 days if not L. 

Rule 9. For Ecclesiastical JDatss. — For the date of the 1st Tisri (Col. 13) add to 
the date of Moled Tisri as many days as rule 3 adds to its ferial. Then, from the 
date of 1st Tisri (Col. 13) subtract 193 days for the 14th Adar or Veadar=Purim ; 
or 177 days for 1st Nisan (ancient New Year's day) ; or 163 days for the 15th 
Nisan = first day of the Passover ; or 113 days for 6th Sivan=Sebuot= Pentecost. 
These are all in the previous year HC, but depend upon the 1st Tisri. Then to 
the date of 1st Tisri add 9 days for 10th Tisri=Day of Atonement ; or 14 days for 
15th Tisri=Feast of Tabernacles ; or 20 days for 21st Tisri=Hosana Raba. Then 
for 25th Kislef add 83 days if the year be s, or S, or o, or O ; but 84 days if it be 1, 
or L, by rule 4. 

4 



HC. 



HC. TABLE. 

EG. Examples AD. 1883 to 1902. 



1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 




4 


i 

to 

oS 
Oh 


o 

3 
■g 




"3 












c3 








a 

<D 
A^ 

03h-3 

a; . 
Lhcq 

II 


1 

© - 

o © 


o 3 ! 
gri 

05 > 


cc 

s a) 

© i—i 

9 

> 


© 

3 
PS 

o 

a 

03 

OJ 


o 
3 3 

¥ 

o 

o3 

A 




^ 3 

a m 

a 2 

©H 


w 

redo 30 

— - »OoO t- 

o • 

gesops 
o 


CO 

© 
PS 

t-i 

<£ 

w 



cc 
Eh . 

jj CO 

.§£§ 

© 


■3 . 
o© 

!| 

d 

E II 

"-hH 


ri 
e3 
CD 

©tJh* 

a S3 

l>> 

A 


a 

■Sri. 

<3 03 OS 
m>H«o 

O ta. "> 
CO 

&H 


Ik 

il- 

© q ^ 

5 © 


1883 


Mar. 23 


April 22 


June 11 


5614 


Oct. 


2 


1 


iii.. 0.. 879 




iii 





354 


Oct. 2 


Dec. 24 


1884 L 


" 11 


" 10 


May 30 


5615 


Sept. 


20 


2 


vii.. 9.. 675 




vii 


1 


355 


Sept. 20 


" 1 


1S85 


" 1 


Mar. 31 


" 20 


5846 


" 


9 


E 3 


iv..l8.. 471 


J 


V 


L 


385 


" 10 


11 3 


1886 


" 21 


April 20 


Jime 9 


5647 


n 


28 


4 


iii.. 15.. 1060 


G 


V 





354 


" 30 


" 23 


18S7 


" 10 


" 9 


May 29 


5648 


" 


IS 


5 


i.. 0.. 856 


A 


ii 


s 


353 


" 19 


" 11 


1888 L 


Feb. 26 


Mar. 27 


" 16 


5649 


" 


6 


E 6 


v.. 9.. 652 




V 


L 


3S5 


" 6 


Nov. 29 


1889 


Mar. 17 


April 16 


June 5 


5650 


" 


25 


7 


iv.. 7.. 161 


A 


V 





354 


" 26 


Dec. 18 


1890 


" 6 


'• 5 


May 25 


5651 


u 


14 


E 8 


i. .15.. 1037 


A 


ii 


S 


383 


" 15 


a 7 


1891 


" 24 


" 23 


June 12 


5652 


Oct. 


3 


9 


vii.. 13.. 516 




vii 


1 


355 


Oct. 3 


11 26 


1892 L 


" 13 


" 12 


1 


5653 


Sept. 


21 


10 


iv..22.. 342 


J 


V 





354 


Sept. 22 


" 14 


1893 


" 2 


1 


May 21 


5654 




' 


11 


Ell 


ii.. 7. 138 




ii 


L 


385 


" 11 


" 4 


1894 


" 22 


" 21 


June 10 


5655 




1 


30 


12 


i.. 4.. 727 


A 


ii 


s 


353 


Oct. 1 


11 23 


1895 


14 10 


9 


May 29 


5656 




> 


19 


13 


v.. 13.. 523 




V 


1 


355 


Sept. 19 


11 12 


1896 L 


Feb. 28 


Mar. 29 


" IS 


5657 




1 


7 


E14 


H..23.. 319 


J 


iii 





384 


" 8 


Nov. 30 


1897 


Mar. 18 


April 17 


June G 


5653 




t 


26 


15 


i..l9.. 908 


J 


ii 


1 


355 


" 27 


Dec. 20 


1398 


8 


" r t 


May 27 


5659 




1 


16 


16 


vi.. 4.. 704 


A 


vii 


s 


353 


k n 


44 9 


1S99 


Feb. 24 


Mar. 26 


41 15 


5660 




' 


5 


En 


iii.. 13.. 500 




iii 





384 


" 5 


Nov. 27 


1900 


Mar. 15 


April 14 


June 3 


5661 




' 


24 


18 


ii.,11.. 9 




ii 


1 


355 


" 24 


Dec. 17 


1901 


5 


" 4 


May 24 


5662 




" 


13 


E19 


vi..l9.. 885 


J 


vii 


s 


383 


14 14 


6 


1902 


" 23 


" 22 


June 11 


"663 





it. 


2 


1 


v. 17.. 394 




V 






Oct. 2 





1883— hi . . . . 879 -Hi . . 16 . 593=(cycle)- 



.17.. -3.) f=Proof, rule 



Then by rules 5, 9, add 9 days to tbe date of 1st Tisri for 10th Tisri=Day of Atonement ; cr 14 
days for 15th Tisri=3uccuf=Feast of Tabernacles, or 20 days for 21st Tir;=Hosana Raba. 

For dates OS., as counted by the Russo-Greeks, subtract 12 days (nominal) from these dates until 
March 1st, A.D. 1900, and then 13 days. And count the holidays as beginning in the evening before 
noon of these dates. 

5 



HCM. 

J7CJf=HEBREW CALENDAR MODIFIED OR MOSAIC. 



HCM. Rule 1. Count all the holidays as beginning in the evening after noon of 
the dates found by rule. (22-26.) 

HCM. Bale 2. Modify HC. Rule 2, thus . Find the embolismic years correspond- 
ing with the given century, by HCM. Rule 6. Then use the present standard date 
II. .5. .204 before HC. 5000 (AD. 1239). Then until HC. 11,500 (AD. 7739) sub- 
tract a lunation (I. .12. .793), leaving the standard vii. .16. .491 as at present, and 
at each period of 6500 years thereafter, continue to subtract a lunation. (27-33.) 

HCM. Rule 3. Count J=Jac7i=10 hours (instead of 18 hours). And B=Betu- 
thakphat II. .7. .589 (instead of II. .15. .589). And G=Getrad III. .1. .204 (instead 
of III.. 9.. 204). 

For ancient dates, omit B, G, and A. 

HCM. Rule 4. For ancient dates, count ISTisan the first month with 30 days, and 
all the months thereafter alternately 29 and 30 days, except the last month, which 
depends' upon the beginning of the next year. And find the length of each year 
from the difference of the 1st days of Nisan. (46-53.) 

HCM. Rule 5. This is the same as HC. Rule 5, except that all the holidays be- 
gin in the evening after noon of the dates found by rule. Or one day later, then 
by HC. Rules 1, 5. (54.) 

HCM. Rule 6. Use HC. Rule 6, with the following 

modifications of the table of GKD. 

a. Substitute this table for dates on and after HC. 5400 
(AD. 1639) until HC. 5700 (AD. 1939). 

b. For future years, when HC. year of change of any 
GN. arrives, then add 6500 to the year of change, and 
subtract 765,433 from its GND., and remove E from the 
previous GN. to that GN". 

c. For past years, add 6500 to the given year HC, and 
if the sum be less than the HC. year of change, then add 
765,433 to the GND., and remove E from that GK. to the 
previous GN. 

d. In all cases, take E and GND. as in this table, when 
not changed as by b, and e above. (63-67, 84-86.) 

HCM. Rules 7, 8, 9, are the same as HC. Rules 7, 8, 9, 
by the previous rules of HCM. 

8 



OC. year 




of 


GN. 


Change. 


E 1 


11,500 


7,400 


2 


9,800 


E 3 


5,700 


4 


8,100 


5 


10,500 


E 6 


6,400 


7 


8,800 


8 


11,200 


E 9 


7,100 


10 


9,500 


11 


12,000 


E12 


7,800 


13 


10,200 


E14 


6,100 


15 


8,500 


16 


10,900 


E17 


6,800 


18 


9,200 


19 



GND. from 
HC. 54C0 
to 5700, or 
from AD. 
1639 to 1939. 



1,002,731 
1,486,080 
1,203,996 
1,68.7,345 
1,405,261 
1.123,177 
1,608,526 
1,324,442 
1,042,358 
1,525,707 
1,248,623 
961,539 
1,444,888 
1,162,804 
1,646,153 
1,364,069 
1,081,985 
1,565,834 
1,283,250 
except the modifications, 



HCM. 



HCM. TABLE MODERN. 



1 


2 


3 


4 


5 


6 


7 

d 

s 


8 


9 


10 


11 


12 


13 


14 




£ 














DQ 












>> 








si 


■>* 














S 




"o 










Ss 

p3 








<D 
















-a 




.o 


















tH 


o 














i> 




a 




GQ 






'<£ 








a 
P 






CS 




> 






to 












.l-J 


o . 
II &0 

o 5 




09 

EH 




P 

P 

< 


< 

1 
a 


"3 
as 

o 
> 


JO 

T 

o 




Jl 




d 

W 

as 


a 
o 

c 




O) 

i 
Pi 

o 




o 
f-l 

o 

o 

a! 

Si 


o 

a 

CO 


VJ 

Eh 
m 

O 

[3 


O II 

Sp' 

o 

— 

il 


>< 

.2 


o 

CO 


as 

§ 

w 

o 
to 


» 






a 




o 




S3 


a 








^ 


"3 


QJ 






as 


aj 


h 


Ph 




Q-, 




P 




£644 


P 




6 




D 


« 


ft 


CO 


p 


P 


P 


1883 


Feb. 


22 


Mar. 


24 


May 


13 


Sept. 


2 


E 1 


i. 


.12. .86 


J 


ii 


S 


383 


Sept. 3 


Nov. 25 


1884 L 


Mar. 


11 


April 10 


u 


3:1 


5645 


" 


2.) 


2 


vii. 


. 9.. 675 




vii 


1 


855 


" 20 


Dec. 13 


1885 


" 


1 


Mar. 


31 


« 


20 


564fi 


(i 


9 


E 3 


iv. 


.18.. 471 


J 


V 


L 


385 


" 10 


" 3 


1S86 


" 


21 


Apr. 


20 


June 


9 


2647 


" 


28 


4 


iii. 


15.. 1060 


JA 


V 


o 


854 


" 30 


" 22 


1S87 


" 


10 


» 


9 


May 


29 


5648 


u 


18 


5 


i. 


. . 856 


A 


ii 


s 


353 


M 19 


" 11 


18S8L 


Feb. 


26 


Mar. 


•2? 


" 


16 


5649 


" 


6 


E 6 


V. 


. 9 . 652 




V 


L 


3S5 


" 6 


Nov. 29 


1889 


Mar. 


17 


Apr. 


16 


June 


5 


5G50 


" 


25 


7 


iv. 


. 7. 161 


A 


V 


o 


354 


" 26 


Dec. 18 


1890 


'« 


6 


" 


5 


May 


23 


5651 


" 


14 


8 


i. 


.15.. 1037 


J 


ii 


1 


355 


" 15 


" 8 


1S91 


Feb. 


24 


Mar. 


26 


K 


15 


5652 


" 


4 


E 9 


vi. 


. 0.. 833 


A 


vii 


S 


^ 


" 5 Nov. 27 


1892 L 


Mar. 


13 


Apr. 


12 


June 


1 


5653 


" 


21 


10 


iv. 


.22.. 342 


J 


V 





3.34 


" 22 Dec. 14 


1893 


" 


2 


> l 


1 


May 


21 


5554 


" 


11 


11 


ii. 


. 7.. 13S 




ii 


1 


355 


" 11 


4 


1894 


Feb. 


20 


Mar. 


22 


" 


11 


5655 


Aug. 


31 


E12 


vi. 


.15. 1014 


J 


vii 


L 


385 


1 


Nov. 24 


1895 


Mar. 


12 


Apr. 


11 


" 


31 


5656 


Sept. 


19 


13 


v. 


.13.. 523 


JA 


vii 


s 


853 


11 21 


Dec. 13 


1896 L 


Feb. 


2S 


Mar. 


29 


(i 


IS 


5657 


" 


7 


E14 


ii. 


.22.. 319 


J 


iii 





384 


" 8 Nov. 30 


1S97 


Mar. 


18 Apr. 


IT 


June 


6 


5638 


" 


26 


15 


i. 


19.. 908 


J 


ii 


1 


355 


11 27 Dec. 20 


1898 


" 


8 


" 


7 


May 


27 


5639 


u 


1(1 


16 


vi. 


. 4.. 704 


A 


vii 


1 


335 


" 17 


" 10 


1899 


Feb. 


26 


Mar. 


28 


cc 


17 


5660 


" 


5 


E17 


iii. 


.13.. 500 


JA 


V 


s 


383 


M 7 


Nov. 29 


1900 


Mar. 


Id 


Apr. 


15 


June 


4 


5661 


" 


24 


18 


ii. 


.11.. 9 


J 


iii 





354 


" 25 


Dec. 17 


1901 


" 


5 


u 


4 


May 


24 


5662 


" 


18 


19 


vi. 


.19.. 883 


J 


vii 


1 


355 


" 14 


" 7 


1902 


Feb. 


23 


Mar. 


25 


" 


14 


5663 


" 


3 


E 1 


IV. 


4.. 681 


A 


V 






" 4 





1883 — i.. 12. .86 cycle ii.. 16.. 595= iv. .4..681=Proof. 



Then to the date of 1st Tisri, add 9 days for 10th Tisri =Day of Atonement, or 14 days for the 
15th Tisri = Succot or Feast of Tabernacles ; or 20 days for 21st Tisri=Hosana Raba. 
Then count the holidays, as beginning in the evening after noon of these dates. 

HCM. Example in AD. 70. 
Noon of 14th. Nisan fell at noon of 14th April AD. 70 as shown by Josephus 
(104-100). Then by HCM. Rule 6 for past dates, prepare the table for the first 

7 



HCM. 



century AD., and AD. 1+3761=HC. 3762 as AD. 101=HC. 3862. To these add 
6500 and the sum HC. 10,262 and 10,362 in each case is less than the year of 
change of GN. 1, 6. 9, 12, 17, so that E must be changed to the previous GIST. 
But they are more than the year of change of G-N". 3, and 14, so that these remain 
unchanged. This makes the embolismic years in the first century AD., to be GN. 
3, 5, 8, 11, 14, 16, 19. And these are the same as in HC. Rule 6 except that E. 
GK 6 should be E. GN. 5, and E. GK 17 should be E. GN. 16. Consequently, 
in the first century AD., HC, takes the same moon as HCM., except in the years 
GN. 6 and GN. 17. Then by HC. Rule 6 : 

AD. 70+3761=HC. 3831 ;--19 leaves GN. 12, which by both rules gives the 
date of Moled Tisri-Sept. 23. .1. .23. .847. Then HC. makes 1st Tisri=Sept. 24 
for two reasons, first, Jack adds one day, because the date reaches 18 hours, and 
setond, Adu would add one day at any hour because the moled falls on day I. 
Then HCM. makes 1st Tisri-Sept. 24 because the date reaches 10 hours, but pays 
no regard to day I. Hence HC. and HCM. agree in making the 1st Tisri= 
Sept. 24, and 14th Nisan= April 13. But HC. Rule 1, makes noon of the 14th 
Nisan fall at noon of April 13 contrary to the historic fact, while HCM. Rule 1, 
makes noon of 14th JSTisan fall at noon of April 14, according to the historic fact. 
And mean full moon fell at 8 hours 37 m a.m. on April 14, AD. 70. This proves 
that HCM. Rule 1, is required for ancient dates. (25, 26, 30, 31, 64-67, 76, 104, 105.) 

COMPARISON OF HC. AND HCM. AD. 26 TO AD. 37. 

Table I.— By the Rules of HC. 



AD. 


GN. 


15th Nisan 
Noon. 


Moled. 


Moled Tisri 
Character. 


Rule 3. 


1st Tisri. 


26 


E 6 


March 23.. vii 


Aue. 31 


vii. 19.. 662 


JA. 


Sept. 2..II 


27 


7 


April 10.. v 


Sept. 19 


vi.,17.. 171 


A. 


'• 20.. vii 


L 28 


E 8 


March 30.. Ill 


" 8 


iv. 1..1047 


A. 


9..v 


29 


9 


April 17.. I 


" 26 


II. 23.. 556 


J. 


" 27.. in 


30 


10 


April 6..v 


" 16 


vii.. 8.. 352 




" 16.. vii 


31 


E 11 


March 27.. I II 


" 5 


iv.,17 . 148 


A. 


" 6..v 


L 32 


12 


April 15 III 


" 23 


III.. 14. 737 


G. 


" 25.. v 


33 


13 


April 4.. vii 


11 12 


vii.. 23.. 53 5 


JA. 


" 14. II 


34 


E 14 


March 23.. Ill 


" 2 


v.. 8.. 329 




" 2 v 


35 


15 


April 12.. Ill 


" 22 


iv.. 5.. 918 


A. 


M 22. .v 


L 36 


16 


March 31. vii 


9 


I.. 14.. 714 


A. 


" io. .n 


37 


E 17 


March 21 . . v 


Aug. 29 


v.. 23.. 510 


JA. 


Aug. 31.. vii 







Table II. 


— By the Rules of HCM 






AD. 


GN. 


15th Nisan 

6 P.M. 


Moled. 


Moled Tisri 
Character. 


Eule 3. 


1st Tisri. 


26 


6 


April 20.. vii 


Sept. 30 


II.. 8.. 375 




Sept. 30.. II 


27 


7 


April 10.. v 


" 19 


vi..l7.. 171 


J. 


" 20.. vii 


L 23 


E 8 


March 29.. II 


" 8 


iv.. 1..1047 




11 8..iv 


29 


9 


April 17.. I 


" 26 


If.. 23.. 556 


J. 


" 27. Ill 


30 


10 


April 6. v 


" 16 


vii.. 8.. 352 




" 16. .vii 


31 


E 11 


March 27.. Ill 


" 5 


iv..l7.. 148 


J. 


11 6..v 


L 32 


12 


April 14.. II 


" 23 


III. 14.. 737 


J. 


" 24.. iv 


33 


13 


April 3..vi 


" 12 


vii.. 23.. 533 


J. 


" 13 i 


34 


E 14 


March 23.. Ill 


" 2 


v.. 8.. 329 




" 2..V 


35 


15 


April 11. II 


" 21 


iv.. 5.. 918 




" 21.. iv 


L 36 


E 16 


March 31.. vii 


" 9 


i. 14.. 714 


J. 


" 10.. II 


37 


17 


April 19. vi 


14 28 


vii. 12.. 223 


J. 


11 29.. I 



HCM. 



Table HI.— By HCM. one Lunation later. 



AD. 


GN. 


15th Nisan 

6 P M. 




Moled Tisri 
Character. 


Rule 3. 


1st Tisri, 


28 


E 8 


iv 




v.. 14.. 760 


J. 


vi 


29 


9 


ni 




iv..l2..269 


J. 


V 


30 


10 


vu 




i. 21.. 65 


J. 


n 


31 


E 11 


iv 




vi.. 5. 941 




VI 


32 


12 


ni 




v.. 3. .450 




V 


33 


13 


i 




II. .12. .246 


J. 


m 


34 


E 14 


V 




vi..21.. 42 


J. 


Vll 



The difference. HCM. removes E from GK 6 and 17 to GN. 5 and 16, and 
omits A, and counts J =10 hours instead of 18 hours ; and the 15th Nisan as 
beginning after noon of the dates found by rule, instead of the evening before 
noon of the dates found by rule. (77-83.) 



HC. NOTES. 



HC.=Hebrew Calendar (present). HCM.=HC. Mosaic (in accordance with the 
ancient rules). 

CONTENTS.* 

1, 2 Character is a measure of time or a date. 
6, 7 Rules by different authors. 

8 Date of construction of HC. 

9 Used since the dispersion in AD. 1040. 
10-12 Mosaic Rule to determine dates. 
13-17 Hebrew astronomic rules. 

18-21 Hebrew astronomic equivalents. 

Rules of HC. and HCM. 
22-26 HCM. Rule 1, makes the holidays one day later than HC. Rule 1. 
27-33 HCM. Rule 2, corrects the solar errors of HC. Rule 2. 
* 34-45 HCM. Rule 3, makes Jach=10 hours instead of 18 hours., and for modern 
dates cuts off 8 hours from G, and B. And for ancient dates, omits 
A, G, B. 
46-53 HCM. Rule 4. For ancient dates makes Msan the first month, of 30 days, 
and thereafter alternately 29 and 30. Different names of the months. 
54 HCM. Rule 5. Ecclesiastical days. The same as HC. Rule 5. 
55-67 HCM. Rule 6, corrects the solar errors of HC. Rule 6. 

68 HCM. Rule 7, to find the ferial, the same as HC. Rule 7. 

69 HCM. Rule 8, to find dates by progression, the same as HC. Rule 8. 

70 HCM. Rule 9, for Julian dates of the holiday, the same as HC. Rule 9. 
71-75 HC. Examples AD. 1833—1902. 

76 HCM. Example AD. 70= Siege of Jerusalem. 
77-83 HCM. Examples AD. 26— 37= date of the Crucifixion. 
84-86 HCM. Examples AD. 1883—1902, corrects solar errors. 

General Remarks. 
87-89 Rabbi Adler, chief Rabbi in Great Britain, on the ancient calendar. 
90-103 Josephus, Historic dates. 
104-106 Conclusions from Josephus. 
107-111 Indefinite dates by Josephus. 

Contradiction, as to 

112 Macedonian months — by Whiston. 

113 Pharmouthi and Xanthicus — by McClintock and Strong. 






* The numbers refer to the paragraphs. For general rules, and for astronomic rules under the 
head MD., see the Appendix, at the end of the work. 

10 



HC. NOTES. 

114 Lord's Supper — by Ussher. 

115 The Seasons — by Ideler. 
116-121 Solar Error of HC— "by Michaelis. 
122-123 Solar Error of HC— by Nesselman. 

124 30 day month of the Deluge — by McClintock and Strong. 
125-126 Date when HC was constructed — by several authors. 
127-130 Prime Meridian of HC— by Muler. 

131 Mosaic date of Easter— by Lindo. 
132-134 Signification of Jack — by Lindo, Scaliger and Muler. 
135-138 Perfection of HC.— by note to Adler. 

HlSTOKY. 

139-150 Facts indicate — that the rule established by Moses to determine the date of 
the Passover was retained until the destruction of the second Temple 
— that Moses retained the Egyptian mode of counting by months of 
30 days. That the present calendar is of Babylonian origin. 
151-156 Contra. Jahn, Seabury, Josephus. 

157-163 Comparison of dates by HC and HCM. from AD. 1883 to 1903. 

Authors. 

Lindo, E. H. Jewish Calendar for 64 years. London, 1838. This I suppose to 
be the present standard authority in English. 

Maimonides. Born AD. 1131. In Vol. 17, Thesaurus Antiquitatum Sacrarum, 
collected by Ugolino, Venice 1755, in Hebrew with a Latin translation in parallel 
columns. This is referred to as standard authority. 

Muler — ISTicolai Muleri. Judoeorum Annus Lunse Solaris, wrote 1636-7. This 
is found in the same volume as Maimonides, in the Astor Library. 

Scaliger. De Emendatione Temporum. 1629. 

Crelle. Journal die Mathematik. 

Slonenski, C H., in Crelle of 1844, p. 179, etc. 

Ideler. Lehrbuch der Chronologie. 

Josephus. "Wars of the Jews AD. 75; Antiquities AD. 93. Translated by 
Whiston. London. 

Long's Astronomy. 

Roman Missal. De festibus mobilibus. 

Brady, John. Clavis Calandria. 

Newton's Chronology. 

Ussher's Chronology. 

Jahn's Eiblical Archaeology. 

Smith's Dictionary of the Bible. 

SchafE's Bible Dictionary. 

Calmet's Dictionary of the Bible. 

Jarvis' Chronological History of the Church. 

Seabury. Theory and Use of the Church Calendar. 

Jackson's Chronological Antiquities. 

Rab. Adler, Chief Rabbi of Great Britain. 

Nesselman (professor) in Crelle. Vol. 26. 

Whiston's translation of Josephus. 

Moore, William, in the Churchman's Year Book of 1870. 

11 



HC. NOTES. 

Farrar's Life of Christ. 

Cruden's Concordance. 

Smyth's Celestial Cycle. 

Almanacs, Hebrew, for current dates. 

Sekles, S. A writer in the Jewish Messenger, supposed to be good authority, as 
to what is found in the Talmud, because at that time Rab. S. M. Isaacs was the 
editor. 

Rev. S. M. Isaacs, a learned Rabbi in New York, to whom I was introduced by 
a letter by the Rev. Marshall B. Smith, D.D., and who referred me to the best 
authorities as above, and gave the following additional names which have not been 
examined, viz. : Hirsh's Horeb, Altona 1887 ; Jost's Geschichte des Judenthums ; 
R. J. Wanderbar, Immerwerender Kalendar der Juden, Dessau 1854 ; Edersheim, 
History of the Jewish Nation, Edinburg 1856 ; Hertzfeld, Geschichte des Folks 
Israel, Nordhausen 1857; Munk's Palestine, 1845. And an old almanac of De 
Sola in Montreal. 

McClintock and Strong's Cyclopedia of Biblical, Theological, and Ecclesiastical 
Literature. This, under the head Calendar, gives the titles of many works on this 
subject. 

Character. 

(1). In the present Hebrew Calendar (HC), and in the present modification 
(HCM.), a character has three terms, 1st Days, 2d Hours, 8d Scruples (or Chela- 
kim or Helakim) of which 1080= one hour, and each =3^ seconds. "When character 
is a measure of time, the first term is the excess of days above even weeks, as in 
the following : 

I. .12. .793=29 d. .12 h. .793 scruples = one lunation. 

IV. .8. .876=354. .8. .876. .= Common year of 12 lunations. 

V. .21.-589=383. .21. .589. . =Embolismic year of 13 lunations. 

II. .16. 595=6939. .16. .595=Cycle of 235 lunations. (29, 30.) 

(2). When character represents a date, the first term I to VII = ferial Sunday to 
Saturday. Thus the standard II. .5. .204=HC. 1, Oct. 7. .Monday. .5 h. .204 scr. 
in Hebrew time counted from the beginning of Monday at 6 hours after noon of 
Sunday, Oct. 6, at Jerusalem. This is called Moled Tohn= Birth of the moon at 
the Creation = first Moled Tisri=GND. of GN. 1 in HC. l=Mean conjunction, with 
wonderful accuracy as determined by calculation. (.27-33, 57, 132-134, 187.) 

(3 to 5). GN,P,Q,R,S. explanation transferred to Appendix. 

Other Rules of HC. 
(6). Maimonides, Scaliger, Muler, Lindo, Nesselman, Sekles, give different rules 
to simplify the calculations in this "labyrinth " as Nesselman calls it. The present 
are presented as more simple than either of the others, and so prepared as to be 
used by rote without the necessity of understanding the reasons, which are given 
below in the form of notes. In all these rules, the smallest measure is a scruple of 
31 seconds, and fractions are never used in calendar calculations. But Scaliger 
(Prol. VI) and (pp. 275-282) says that : "Rabbi Adda, the most ancient teacher of 
the Jews, .... defines the year to be 365 days 5 h . .997 scr. and 48-:- 76 scruples." 
And Scaliger (pp. 276-278) gives annual tables with this fraction, and says that 
Epiphanius writes the name Rabbi Ada. And calculation shows that this length 
of the year is the 19th part of 235 lunations without a fraction. (7.) 

12 



^ 



HC. NOTES. 

(7). C. H. Slonenski (Crelle of 1844, p. 179) gives a rule in decimal fractions. 
But these measures cannot be reduced to decimals without interminable fractions 
which must be increased or diminished to find the result. This may cause the dif- 
ference of a scruple at the turning-point. And that may cause the difference of a 
day from the standard rule by characters. And that may be increased to three 
days by the rules of transfer. Hence a rule in decimals is not reliable, although 
such extreme cases may never occur. (6.) 

The Present Calendar. 

(§). "The present calendar is of unknown origin," says Professor Nesselman 
(Crelle, V. 26, p. 50). This is obviously the fact from the different years assigned 
as its date. A note to Maimonides (Col. 274) gives the supposed years AD. 353, 
369, 424, 525. Scaliger (p. 123) supposes AD. 345. Prideaux (Seabury, p. 72) says 
AD. 360. Lindo (Introduction) says that some suppose AD. 325 [the year of the 
Council of Nicea] ; that the authors of the Encyclopedia say AD. 360, while others 
say AD. 500. That the Mishna AD. 180 is the first work we have on calendars. 
That we take the calculations of Rab. Ada, who was born in Babylon AD. 188. 
And that from these data Rab. Hillel AD. 352 [?] framed the tables used at 
this day. 

(9). From internal evidence, it appears to have been based upon the solar and 
lunar facts in AD. 607. But the date of its construction is of no practical import- 
ance. The important fact is, that it did not come into general use until AD. 1040, 
when the Jews were expelled from Asia by order of the Califs, and became scat- 
tered through Europe. From that date, the present rules must necessarily be fol- 
lowed to find corresponding dates. But for ancient dates they must be so modified, 
as to agree with the : (6, 14, 125, 126.) 

Mosaic Rule. 

(10). Moses gives specific directions, as to what is to be done on the 14th day of 
the First Month (Ex. xii. 3-6). But he does not specify, how this date is to be 
"■• determined. Maimonides (Col. 234) believes that the Mosaic rule was handed down 
by tradition. Ideler (p. 213) says : "From the Talmud and from Maimonides, we 
see, that during the second temple, the beginning of the month was yet always 
determined by immediate observation." (12, 25, 26, 76, 87, 88, 94-103.) 

(11). As to the specific mode. The first day of Nisan was "consecrated," as 
,the beginning of the year, in the evening after the first appearance at Jerusalem, 
of the new moon, which would bring the full moon of Nisan at the same date as 
■the vernal equinox or within one lunation thereafter. But if clouds obscured the 
new moon, so that on the day of its calculated appearance, it was not actually seen 
!by two credible witnesses before sunset, then the Sanhedrim postponed the begin- 
ning of the year to the next evening. And occasionally when the crops were back- 
ward, the Sanhedrim postponed the beginning of the year to the next new moon. 
See Maimonides, Thesaurus ilntiquitatum (Vol. 17, Col. 236, 275). Long's Astron- 
omy (Sec. 1252-1255). Roman Missal (De festibus mobilibus). Scaliger, De Emen- 
datione temporum (pp. 121-135). Crelle, Journal die Mathematik (Vol. 26, p. 
50). Brady, Clavis Calandria (p. 295). Jackson's Chronological Antiquities (Vol. 
2, p. 20). Ideler, Lehrbuch der Chronologie (p. 213). Jahn's Biblical Archaeol- 
ogy (Month). Cruden's Concordance (Month). (66, 87, 88.) 

(12). Now : MaimGnides (Col. 236) says : " Each month the moon is occulted and 

13 



HC. NOTES. 

does not appear for about two days, more or less, to wit, at the conjunction with the 
sun before the end of the month. Then again it is seen in the evening in the West. 
But in the night in which the moon first appears after its occultation, from that the 
beginning of the month is counted." And (Col. 234) he believes this to be the 
Mosaic rule. And Scaliger (Prol., p. 7) says that the moon rarely appears before 
the second day after conjunction. And -Newton and Smyth, say that the moon 
has never been seen earlier than 18 hours after conjunction. And since full moon 
is 14 days 18 hours after conjunction, Nisan could not possibly begin before 18 
hours after conjunction. Nor could full moon fall later than the end of the 14th 
Nisan. These are astronomic dates to be determined by astronomic rules, as 
follows. (Newton, Vol. 5, p. 394 ; Smyth, Yol. 1, p. 123.) 
Hebrew Lunar Dates. 

(13). All Hebrew lunar dates are — or may be — determined, by the constant addi- 
tion of a lunation of 29 d. .12 h. .793 scr. to the standard date HC. 1, Oct. 7. .5. . 
204. And the date of any new moon in any year, can be found by adding such 
lunations to the date of Moled Tisri found by rule. In AD. 607, HC. makes the 
date of Moled Tisri Aug. 28. .16 hours exactly, while MDB. makes the date of 
mean new moon counted in Hebrew time from 6 hours before midnight at Jeru- 
salem, = Aug. 28.668,798=3 min. 4 sec. more than 16 hours. This proves that in 
AD. 607, the date of Moled Tisri, is the date of mean conjunction counted in He- 
brew time from 6 hours before midnight at Jerusalem, and that 18 hours signifies 
mean conjunction falling at noon of the day of the month and of the week found 
by rule. (14, 18, 56-58, 125, 126.) 

(14). The date of Moled Tisri is assumed to be in all cases the date of mean 
conjunction in Hebrew time, although there is a slight difference from the latest 
determination of the length of a mean lunation. The HC. lunation of 29. .12. .793 
is less than half a second (0.432) per lunation, or less than 5£ seconds (5.3432) per 
year more than 29.530,589. Starting from AD. 607, this makes the dates earlier 
when going backwards, and later in going forwards. Thus in AD. 33, HC. makes 
the date of Moled Tisri Sept. 12. .23. .533. And MDB. makes the date of mean 
conjunction in Hebrew time, Sept. 13.017,487. So that HC. makes the date 55 m. 
34 sec, earlier than MDB. Then AD. 1883, HC. makes the date of Moled Tisri = 
Oct. 2..0..879. Subtract 64 lunations, leaves full moon March 24.. 2.. 44, or 
March 24. .2 h. .2 m. .27 sec, while MDB. gives the date of mean full moon= 
March 24.006,156=March 24. .0 h. .8 m..52 sec. So that in AD. 1883, HC. 
makes the lunar date=l h. .53 m. .35 sec, more than by MDB., while in AD. 607 
it was 3 m. .4 sec. less. And MDB. is proved to be correct. This makes the HC. 
lunation come so near to the latest determination, that the lunar dates by HC, 
are assumed to be perfect for all time, and when practicable are used instead of 
the dates by MDB., to prove the necessity of the modifications by HCM. And 
this wonderful lunar accuracy at the early date of Rab. Ada (or Adda), who was 
born in Babylon AD. 188, and is said to have furnished the data for HC, may be 
attributed to his access to the records of the Era of Nabonassar (NE.), from which 
we obtain the date of an eclipse at Babylon 2600 years before AD. 1880, which is 
used at the present time, to determine the precise length of a mean lunation. (2, 8, 
MD., 2d Ex. in A.) 

Hebrew Solar Dates. 

(15). No solar date is given specifically in HC. All the dates are lunar, and 
these are almost perfect. The solar date depends upon the selection of the new 

14 



HC. NOTES. 

moon 5£ lunations after the full moon which falls on, or next after the vernal equi- 
nox, so that the full moon 5| lunations before the new moon of Tisri shall be the 
full moon of Nisan, which by the Mosaic rule, must fall within one lunation after 
the vernal equinox. This solar date is determined by the selection of the proper 
moon at the beginning of each cycle. "Within the cycle the solar date is determined 
by the arrangement of the embolismic years. And this follows as a necessary 
consequence, when the date of the earliest moon is determined. (12, 14, 27-33, 49, 
55-62.) 

(16). The earliest solar date in HC, is that of GK 17. And AD. 607=GN. 17. 
And in AD. 607, MDB. makes the mean full moon fall 0.014912 day =22 min- 
utes after the mean equinox. Consequently in AD. 607, the whole series of 19 
full moons fell within one lunation after the vernal equinox. And the lunar date 
varied only 3 min. 4 sec. from the mean date of New moon in Hebrew time 
according to MDB., which has been proved to be correct. So that in AD. 607, 
both solar and lunar dates agreed precisely with the Mosaic rule. (57, 125, 126, 
MD. 2 Ex. in A.) 

(17). But HC, assumes that 235 lunations of 29 d. .12. .793 are exactly equal to 
19 equinoxial years. This makes the solar year 365.246,822 days=365 d..5 h. . 
997 scr. +48-5-76 of a scruple, which Scaliger (Prol., p. vi) says that " Rabbi Adda 
. .defines the year to be." This is 6 minutes 38 seconds more than 365.242,216, the 
mean year of MDB. And this causes HC to put the Passovers represented by 
GIST. 6 and GN. 17, in the month Adar (one lunation too early) for the ancient rule 
in the first century AD., and those represented by GN. 1, 9, and 12 to be one luna- 
tion too late since AD. 1630. And the Passover represented by GN. 4 will follow 
them into the month Zif in AD. 1972. But in consequence of the accuracy of the 
lunar dates, the mean date of the moon will be given very nearly, whether it be 
the moon of Adar, or of Nisan, or of Zif. (10-12, 14, 27-33, 63-67, 77, 126.) 

Hebeew Equivalents. 

(1§). For Hebrew time counted from 6 hours before midnight at Jerusalem, add 
0.348,148 day, to standard time counted from midnight at Greenwich. Then for 
true mean time by HC, add 1 hour, 53 min., 35 sec. in 1883, and thereafter add 
5.3432 seconds per year, to the Hebrew time. (2, 14, 65, 89.) 

(19). For the date of the new moon of Msan, subtract 177 d. .4 h. .438 scr. (6 
lunations) from the date of Moled Tisri. 

(20). For the date of the full moon of Nisan, subtract 162 d. .10 h. .42 scr. (5£ 
lunations) from the date of Moled Tisri. 

(21). For the age of Moled Tisri, subtract the hours and scruples of its date from 
24 hours. And for the age of the new moon of Msan add 4 h . . 438 scr. to the age 
of Moled Tisri— because from 1st Nisan to 1st Tisri=177 days, and 6 lunations= 
177 d.. 4 h.. 438 scr. 

Explanation of the Rules. 

With proofs that the modifications of HCM. are required for ancient dates. 

(22). HC. Rule 1. " The holiday begins in the evening before noon of the date 
found by rule." Maimonides is the only known author who states this distinctly. 
He says (Col. 280) : "If the date fall a moment before noon, the calendar is cele- 
brated on that day." Muler (Col. 55) says, of the standard date II. .5. .204, that it 
signifies : " The second day of the week 5 h . .204 sc. after G hours of the evening, 

15 



HC. NOTES. 

i. e., after the beginning of the second day." This is shown by current dates in 
Hebrew almanacs. Lindo says that in 1825 and 1903, the Passover and Easter fall 
on the same day. In these years Easter falls on the day of full moon. Nesselinan 
says that Passovers fall on the day of full moon. (24, 122, 123, 131.) 

(23). HCM. Rule 1. " The holiday begins in the evening after noon of the date 
found by rule." Because : Astronomical calculation proves, that with wonderful 
accuracy, the date of Moled Tisri is the date of mean conjunction in Hebrew time 
counted from 6 hours before midnight at Jerusalem. And when the Moled falls at 
18 hours, mean conjunction falls at noon of the day of the week and of the month 
found by rule. By HC. Rule 3, the 1st Tisri has the same date as the Moled, if 
the Moled fall a scruple less than 18 hours, or noon. So that HC. Rule 1, makes 
Tisri begin a scruple less than 18 hours before conjunction. And this makes Nisan 
begin a scruple less than 13 h. .642 scruples before conjunction. And it makes full 
moon fall on the 15th Nisan. These were all impossible under the Mosaic rule. 
(10-14, 22-26, 36, 76.) 

(24). This can be shown by any common almanac as for New York in 1864. 
Full moon at New York fell April 10th 6 h. .48 m. a.m. Add 7 h. .17 m. for 
longitude makes full moon at Jerusalem April 10th. .2 h. .5 m. p.m. Both HC. 
and HCM. make the 14th Nisan fall on April 9. By HC. Rule 1, the 14th Nisan 
begins at 6 p.m. of April 8, and full moon falls 20 h. .5 m. after the end of 14th 
Nisan, and hence 20 h . . 5 m. later than was possible under the ancient rule, while 
HCM. Rule 1, makes full moon fall 3 h. .55 m. before the end of the 14th Nisan, 
in accordance with the ancient rule. (10-14, 71, 84.) 

(25). This result from astronomic calculation is proved to be the ancient rule by 
the historic statement by Josephus, who was present at the time, and shows that in 
AD. 70 noon of the 14th Nisan was noon of April 14. Both HC. and HCM. make 
the 14th Nisan fall on April 13. By HC. Rule 1, the 14th Nisan ended in the even- 
ing of April 13, contrary to the historic fact. By HCM. Rule 1, the 14th Nisan 
began in the evening of April 13 and ended in the evening of April 14, in accord- 
ance with the historic fact. (76, 104-105.) 

(26). This Passover of AD. 70, was the last that was ever held in the Temple at 
Jerusalem, when the Hebrews ceased to be a nation. Such a remarkable fact was 
doubtless subjected to calculation by the unknown author of this calendar. And 
as doubtless he intended his rules to be interpreted in accordance with HCM. Rule 
1. (8, 76, 87-89, 104-105.) 

(26 V). The Paschal Canons of the 5th century show that the day of full moon 
was counted the 14th day of Nisan. (AC. Notes 1-11.) 

(27). HC. Rule 2. "The embolismic years are the same for all time." This as- 
sumes that 235 lunations are exactly equal to 19 solar years. (15-17, 27-33.) 

(2§). HCM. Rule 2, finds from the latest determinations that 235 mean lunations 
are 0.086,311 day more than 19 mean years. Hence a full moon represented by 
any GN , after becoming the full moon of Adar, advances at the rate of 0.004,542, 
68 day per year, and in 6500 years after it became the full moon of Adar, falls at 
the date of the vernal equinox and becomes the full moon of Nisan. It remains the 
full moon of Nisan while continuing to advance, for 6500 years, when it passes the 
limit of one lunation after the vernal equinox and becomes the full moon of Zif , 
when the next earlier moon in the same year (after keeping the same distance during 
its advance through Adar), reaches the date of the vernal equinox and becomes the 

16 



HC. NOTES. 

full moon of Nisan, at the same time that its predecessor reaches the distance of 
one lunation after the vernal equinox and becomes the full moon of Zif . (13, 14, 
17, 30, 31, 63-67.) 

(29). Now, HC. is so accurate in its lunar dates, that it will always give the true 
date of this full moon, whether it be the full moon of Adar, or of Nisan or of Zif. 
But the Mosaic rule required the date of the full moon of Nisan. And by chang- 
ing the embolismic years, HOM. adopts a full moon as soon as it has passed through 
Adar and reached the date of the vernal equinox, and 6500 years thereafter, 
abandons that moon when it becomes the full moon of Zif and substitutes the moon 
one lunation earlier. (10-14, 63-67.) 

(3©). In AD. 607, HC. Rule 2 gave the correct dates of all the full moons of 
Nisan. But at the present time (AD. 1630 to AD. 1927) the full moons represented 
by GN. 1, 9, 12, fall in the month Zif. And the 16 remaining moons of HC. will 
follow into the month Zif at the rate of one moon in 342.1 years. Going backwards 
the case is reversed, and HC. gives the dates of the full moons of Adar at the rate 
of one moon in 342.1 years. In the first century AD., HC. takes the moons of 
Adar in the years GN. 6 and GN. 17, while all the others were the moons of Nisan, 
as shown in HCM. Example AD. 70. And in AD. 70 HC. makes full moon fall 
13 h. .45 m. after 6 p.m. of April 13, while MDB. makes it more correctly 14 h. . 
37 m. This difference is not material. But HC. Rule 1 makes the 14th Nisan 
begin at 6 p.m. of April 12, so that full moon falls 13 h. .45 m. after the end of the 
14th Nisan contrary to the ancient rule, and contrary to the fact, as stated by Jo- 
sephus, who was present at the time. (13, 14, 18, 64-67, 80, 81, 125, 126.) 

(31). Josephus wrote his Wars of the Jews in AD. 75. And AD. 75=GN. 17. 
He states no facts respecting that year to prove that HC. puts the Passover in the 
month Adar, as determined by the general principle of HCM. Rule 6, and as stated 
above. This can be proved by independent calculation, thus. HC. makes Moled 
Tisri fall Aug. 30 ...8. .620, and hence the full moon of Nisan March 20. .22. .578. 
MDB. makes that full moon fall March 20.974,938, and the vernal equinox March 
23.376,734. So that HC. makes the full moon of Nisan fall 2.401,796 days before 
the vernal equinox. And that by the ancient rule, was the full moon of Adar. 
(10-12.) 

(32). HGM. Bute 2, refers to Rule for the changes in the embolismk years, 
because more evident, since any GN. is necessarily E if the next GND. is greater. 
But in Rule 6 this indication of an embolismic year is not required, since each 
GND. is independent of all the others. (57-59.) 

(53). IICM. Bide 2, subtracts a lunation from the standard date in HC. 5000, 
and in each 6500 years thereafter. This assumes that the lunar dates by HC, are 
precisely correct for all time. But it corrects the solar error, by substituting a 
moon one lunation earlier, when the moon of GN. 1, passes the limit of one luna- 
tion after the vernal equinox, and becomes the moon of Zif. This occurred in 
HC. 5000, or exactly HC. 5049 (AD. 1288). And this change is required only when 
GN. 1 passes the limit, for by HC. Rule 2, the date of GN. 1 is first found, and 
this determines the date of each of the 235 moons in that cycle. The changes 
within the cycle are produced by the changes of E. By Rule 6, for future years, 
the change of E from the previous GN. to that GN. , takes a lunation from the 
previous GN. and adds it to that GN. and makes that GN. fall one lunation earlier, 
without affecting the beginning of any other year. The reverse is the case for past 

17 



HC. NOTES. 

years. And there is no provision for adding a lunation to GN. 1 for past years, 
since this would only be required 6500 years before HC. 5000 or 1500 years before 
HC. 1. And these embolismic years are the necessary consequences of the earliest 
GN. (1, 10-16, 28-32, 58, 59, 65, 66, 125, 126.) 

(34). EG. Rule 3. Maimonides (Col. 282) gives the rules without the names or 
explanations, except that 18 hours == noon. Lindo, explains Adu. Muler (Col. 82) 
gives the names and says that they are Hebrew numerals which are used to assist 
the memory. He says that Jac7i=18 hours, and transfers the date to the next day, 
but does not explain the reason. Neither does Scaliger explain the reason. Muler 
(p. 87) and Scaliger (pp. 131-132) explain the reason for Getrad and Betuthakphat, 
as below. (132-134, 137.) 

- (35). HGM. Rule 3. Substitute 10 hours for 18 hours= Jack. With the present 
interpretation by HC. Rule 1, the transfer at 18 hours allows the holidays to fall 
two days earlier than by the Mosaic rule. And by the modification by HCM. 
Rule 1, 18 hours allows them to fall one day earlier than by the Mosaic rule 
Thus, when Moled Tisri falls at 18 hours, mean conjunction falls at noon. Then 
at 24 hours (the end of the day) the moon will be 6 hours after conjunction. The 
moon of Nisan is 4 h. .438 scr. earlier than the moon of Tisri, so that when the 
new moon of Tisri falls at 18 hours the new moon of Nisan will be 10 h. .438 scr. 
old at the end of the day. And this allows full moon to fall 7 h. .1038 scr. after 
the end of the 14th Nisan. The new moon has never been seen earlier than 18 
hours after conjunction. By substituting 10 hours for 18, Nisan cannot begin 
earlier than 18 h. .438 scr., after conjunction. Nor can full moon fall later than 
the end of the 14th Nisan, with the interpretation of HCM. Rule 1. This adds 
one day to the dates by HC. if the hour be between 10 and 18. Thus, for 
example : 

(36). In the examples AD. 26 to AD. 37, both rules make the Moled Tisri fall 
AD. 31 Sept. 5 . . 17. . 148. Consequently the full moon of Nisan fell 10 hours 974 
scruples before noon of March 27. Hence by the Mosaic rule March 27 was the 
14th Nisan. Then both rules make the 15th Nisan fall on March 27. But HCM. 
Rule 1 makes the 15th begin at the end of the day in the evening of March 27, so 
that noon of March 27 is noon of the 14th Nisan, while HC. Rule 1 makes noon of 
March 27 to be noon of the 15th Nisan. And it makes the astronomic date the 16th 
Nisan, but transfers the date one day because the Moled Tisri happens to fall oa 
Day iv= 

(37). Jach can be obliterated thus : Add 6 hours to the standard date, and to 
the rules of transfer which depend upon time and to all the GND. in Rule 6. 
Then 18+6=24 and Jach disappears. This would make the date of Moled Tisri 
count from noon instead of 6 p.m. of the previous day as at present. In like man- 
ner, the 10 hour substitute can be obliterated by adding 14 hours instead of 6. 
Then the date of Moled Tisri would count from 8 hours before noon instead of 
6 hours after noon of the previous day. These are actually better because more 
simple, than the present rules, and the rules were first framed in this form. But 
the old standards were restored to prevent confusion, when dates by these rules 
shall be compared with dates by other rules of this, the most complicated of all 
calendars. But a most interesting study, to determine by calculation, what were 
the intentions of its unknown author. (2, 8, 34-36, 125, 126, 132-134, 137.) 

(38). HGM. Rule 3. Adu, i, iv. .vi. If for any cause the 1st Tisri would fall 

18 



HC. NOTES. 

on day i, iv, vi, then add one day, to prevent noon of the Passover falling at noon 
of day ii, iv, vi. 

(39). Lindo (Introduction) says : " On the same day of the week as the — 
1st day of the Passover are the Feasts of Tamus and Ab ; 2d day are 1st day of 
Sebuot and Hosana Raba ; 3d day are New Year and Tabernacles ; 4th day is 
Rejoicing of the Law ; 5th day is Kipur, the day of Atonement. Consequently if 
the first were ii, Purim would be vii and Kipur vi, upon which neither could be 
observed. If iv, then Kipur would be i, on which it cannot be held, since it has 
the same strict ordinances as the Sabbath. If vi, Hosana Raba would be vii, a 
day upon which its ceremonies could not be held." (40, 71-75, 84-86.) 

(40). HGM. Rule 3. For ancient dates, omit Adu. Sekles says : " All these 
reasons for excepting these days of the week for New Year and the Passover, have 
however not the least foundation either in the Bible or the Talmud. But, on the 
contrary, it appears from different statements in the Talmud, that during the time 
of the second Temple, the holidays were celebrated any day of the week, and the 
only guide to them was the visibility of the Moled, and the exceptions only origi- 
nated with the introduction of the present system." (38, 76, 82, 80, 87, 88.) 

(41). HG. Rule 3. B=Betuthahp7iat=\i .15. .589 (reversed). This adds one 
day to the date next after an embolismic year to prevent the emboiismic year being 
too short for the artificial restriction to three different lengths, as explained by 
M'dler (p. 87). Thus : If the character of an embolismic year be hi. .18 or more add 
the character of an embolismic year v. .21. .589 making ii. .15. .589 or more, as 
the character at the beginning of the next year. Then, at the beginning JA. trans- 
fers iii. .18 to v, and at the end, B transfers ii to hi. Then (Rule 4) v from ill 
=v=index of a short embolismic year of 383 days. It would be 382 days without 
B. Then : 

(42). HGM. Rule 3. B=ii. .7. .5S9. This cuts off 8 hours from B=ii. .15. . 
589, to produce the same effect, after cutting off 8 hours from Jach and using 10 
instead of 18 hours, for astronomical reasons. 

(43). JIG. Rule 3. G=Getrad=iii 9. .204 or more, at the beginning of any 
common year, transfers the date two days to prevent that common year being too 
long for the artificial restriction to three different lengths. Thus to iii.. 9.. 204 
or more, add the character of a common year iv. .8. .876= vii. .18 or more. Then 
G at the beginning transfers iii to v, and JA. at the end transfers vii to ii. Then 
v from ii=iv, which is the index of an ordinary common year of 354 days. It 
would be 356 without G. 

(44). HCM. Rule 3. G=iii. .1. .204 or more. This cuts off 8 hours from hi 
. . 9 . . 204, to produce the same effect after cutting off 8 hours from Jach for astro- 
nomical reasons. 

(45). HGM. Rule 3. For modern dates use A=i, iv, vi, and J=10 hours, and 
B=ii. .7. .589, and G=iii. .1. .204. But for ancient dates use only J =10 hours, 
and omit A, B, G. Sekles says that they were introduced with the present calen- 
dar. And it is obvious that B, G, could not have been used when dates were 
determined by the actual appearance of the new moon of Nisan. 

(46). HG. Rule 4. Count as in the table. 

(47). HGM. Rule 4. For ancient dates count Msan as the 1st Month, and there- 
after the months alternately 29 and 30 days. 

(48). Professor Nesselman (Crelle, Y. 26, p. 50) says: "I know not, when the 

19 



HC. NOTES. 

beginning of the year was changed to Tisri." Eight of these months are named in 
the Bible, and six of them count from Nisan as the first, viz.: Nisan 1st (Esth. hi. 
7); Zif 2d (1 Kings vi. 1); Sivan 3d (Esth. viii. 9); Elul (Neh. vi. 15); Ethanim 
(1 Kings viii. 2) ; Bui 8th (1 Kings vi. 88) ; Tebeth 10th (Esth. ii. 16) ; Adar 12th 
(Esth. hi. 7). (52-53, 112, 149, 150.) 

(49). This change is nominal. It complicates the rules, but makes no change in 
the dates. In Bible times the whole year depended on the date of 1st Nisan. Now 
the whole year depends upon the date of 1st Tisri. But the object of the present 
calendar, is to give the Mosaic date of the 1st Nisan, by means of the date of the 
subsequent 1st Tisri, which is uniformly 177 days later, while 6 lunations are 
177 d. .4. .438, so that the moon falls 4 h. .438 sc. earlier in Nisan than in Tisri, 
and its date in Tisri, determines its date in Nisan. (10-12, 15, 21.) 

(50). The changes in the number of days in Hesvan, and in Kislev, form a part 
of the artificial arrangement of HC. Rule 3, to keep the years within the artificial 
limits of six different lengths. Such rules were not required when dates were 
determined by the actual appearance of the New Moon of Nisan. (10-12, 87, 88.) 

(51). As to S, O, L and s, o, 1, 0=vi=the index of an Ordinary embolismic 
year, because vi comes nearest to the days in the character of an embolismic year 
=v. .21 . .5S9. And o=iv=index of an ordinary common year because iv comes 
nearest to the character of a common year iv. .8, 876. And O, o, are called regu- 
lar, L, 1, perfect, and S, s, imperfect years. And months of 30 days are called 
full, and of 29 days hollow. 

(52). These months are known by the following Hebrew names, which fall in two 
Julian months and two corresponding Macedonian months, of which the first are 
here given, viz.: 1st, Nisan, Mssan, Abib= March =Dystrus. 2d, Iyar, Ijar, Yair, 
Yiar, Zif— April— Xanthicus. 3d, Sivan, Siwan=May=Artemisius. 4th, Tamuz, 
Tammus, Tamus, Thamus=June=Dcesius. 5th, Ab=July— Panemus. 6th, Elul 
=August=Lous. 7th, Tisri, Tishri, Thisri, Ethanim=September=Gorpiceus. 8th, 
Hesvan, Chesvan, Marchesvan, Bul=October=Hyperberetceus. 9th, Kislev, Kis- 
luv, Chislev, Caslev= November =Dius. 10th, Tebeth, Tebet, Teveth= December 
=Apellceus. 11th, Sebat, Shebat, Schebat, Shevat=January=Audynceus. 12th, 
Adar = February— Peritius. The intercalary Ye Adar, Yeadar. (48, 53, 112, 
149, 150.) 

(53). Scaliger (p. 242) gives these Syro-Greek names of the months with their 
Roman equivalents, and says: "Josephus in his notation of Roman times and 
affairs, uses the Macedonian names of the Julian months. In all cases, these agree 
with the Roman months as to the number of days, but differ only in the beginning. 
The Romans begin from January, but these from Hyperberetoeus or October." 
(52, 112, 113.) 

(54). HC. Rule 5 and HCM. Rule 5 are the same, excepting the interpretation 
by HC. Rule 1 and HCM. Rule 1. 

(5§>). HC. Rules 6, 7, and HCM. Rules 6, 7, are translations of HC. Rule 2 and 
HCM. Rule 2, into Julian dates, and all the remarks as to principles, apply to 
them, as in the discussion of HC. Rule 2 and HCM. Rule 2. These rules are orig- 
inal. (27-33, 53-37, 137, 138.) 

(5®). HC. Rule 6. Construction of the table. Reduce every quantity to scruples, 
of which 25920=one day, and 1080=one hour. And 765,433=one lunation oi 
29.. 12. 793. (1.) 

20 



HC. NOTES. 



(57). The standard date Oct. 7. .5. .204= Aug. 68. .5. .204=1,768,164 scruples 
=GND. of GK 1. Then 12 lunations of 765,433=282,084 less than a Julian year 
of 365 days 6480 scruples. Hence 282,084 is the epact or the amount that 12 luna- 
tions recede per year, in Julian time. Then by authority, GN. 17 is the earliest GK 
And GK 17 is 16 years after GK 1. Then 16x282,084-^765,433=5 lunations, + 
686,179 earlier than GND. 1. Subtract 686,179 from the standard 1,768,164 
leaves 1,081,985 the GND. of GK 17, and the earliest GK All the other GND. 
can be found in the same manner, but each would be independent of all the others, 
and might be erroneous. The safer mode is to proceed by progression, where the 
error of one would vitiate all that followed and be shown by the result. Then : 



(5§). Subtract 282,084 from the GND. of any GK, to find 
the GND. of the next GK, except this make the GND. less 
than the limit. • In that case add 483,349 (=765,433-282,084), 
and mark with E, the GND. to which 483,349 is added. Thus 
continue until the GND. of the original GN. is found. Sub- 
tract the GND. of the first, from the GND. of the last and the 
first must be 1565 more than the last, because 235 lunations of 
765,433 scruples are 1565 scruples less than 19 years of 365.25 
days, which are called Solar years by Maimonides. (1, 60, 61.) 



(59). Mark with E, each GN. which preceded the GN. which had a lunation 
added. Or any GN. is E, if the next GND. be greater. (32.) 

(6©). Rule 6. Use of the table. The number of past cycles is multiplied by 1565 
and the product subtracted from any GND. in that cycle, because the Hebrew 
lunations recede 1565 scruples per cycle when measured in artificial Julian 
time. (58.) 

(61). Subtract one from the year HC, so that when R is divided by 4, the sec- 
ond R may be JC. 0, JC. 1, JC. 2, JC. 3. Then JC.x6480=JCC, which added 
to minimum Julian time=calendar (or ordinary) time. And HC. 1, Oct. 7 is JC. 
0, after Feb. 29, and therefore minimum Julian time. 

(62). "Divide the sum by 25920," i.e., the number of scruples in one day. 
And before adding NS. SC. it is necessary to know whether at that date and in 
that nation, dates were counted in OS. or NS. All counted in OS. until Oct. 5-15, 
AD. 1582. The Russo-Greeks still count in OS., as did the English until Sept. 
4-15, AD. 1752. (See NS. Introduction.) (57,81.). 

(63). HCM. Rule 6. This table is constructed by progression upon the same 
principle as HC. Rule 6. Then GND. of GN. 1=1,002,731 is one lunation less 
than 1,768,164 in HC. And GND. 961,539 of GN. 12 is one lunation less thau 
1,726,971 of HC. and is the earliest GND. These by progression produce 1,042,358 
the GND. of GN. 9=one lunation less than 1,807,791 of HC. And the GND. of 

21 



Limit 
Epact 


1,081,985 

-282,084 
+483,349 


GN. 
1 


GND. 

1,768,164 

-282,084 


2 

E 8 


1,486,080 

-282,084 

1,203,996 

+483,349 


4 


1,687,345 


E 19 

i 
1 


1,283,250 

+483,349 
1,766,599 

1,768,164 

-1565 



HC. NOTES. 



AO. 


HC. 


GN. 


year of 


year of 


E = 


Coin. 


Change 


£mb. 

E 1 


1288 


11,500 


3683 


7,400 


2 


6077 


9,800 


E 3 


1972 


5,700 


4 


4367 


8,100 


5 


6762 


10,500 


E 6| 


2656 


6,400 


7 


5051 


8,800 


8 


946 


11,200 


E 9 


3341 


7,100 


10 


5735 


9,500 


11 


1630 


11,900 


E12 


4025 


7,800 


13 


6420 


10,200 


E14 ! 


2314 


6,100 


15 | 


4709 


8,500 


16 ! 


7104 


10,900 


E17I 


2999 


6,800 


18 


5393 


9,200 


19 | 



GXD. 

from IIC. 

5400 io 57 



1,002,731 
1,486,080 
1,203,996 
1,687,345 
1,405,261 
1,1*3,177 
1,606,526 
1,324,442 
1,042,358 
1,525,707 
1,243,623 
931,539 
1,444,888 
1,162,804 
1,646,153 
1,334,069 
1,0S1,985 
1,565,334 
1,283,250 



GN. 1, 9, 12 are the only differences between the GND. of HC. and HCM., with 
the same effect as the changes in Rule 2. Then to show the necessity of these, 
and other changes, and the years of change, take the following. (28-33, 57, 
58, 67.) 

(64). HCM. Rule 6. Years of change, to determine : 

19 years of 365.242,216 days=6939.602,104 days. 
And 235 lunations of 29.530,589 days=6939.688,415 
days. The difference 0.086,311 divided by 19= 
0.004,542,68 day per year, that a moon represented 
by any GIST, advances in equinoxial time. This into 
29.530,589 days=6500.697 years for the full moon 
of each GN. to advance a full lunation after the 
vernal equinox, and to become the moon of Zif 
while the moon one lunation earlier in the same 
year coincides with the vernal equinox. And 6500 
years divided by 19=342.1 years interval between 
the dates of the different GIN", as they pass the limit 
of one lunation after the vernal equinox. And to 
find the order in which they pass the limit reverse 
the rule of GN., and beginning with any GIST. 
continue to add 11 or to subtract 8. And the rule 
of GN. is to add 8 in a circle of 19, i. e., add 8 or 
subtract 11, because the next later GND. is 8 years 
later in a circle of 19 years. (16, 17, 28-33, 58-64.) 

(65). Now, AD. 18S3=GN. 1. In AD. 1883 MDB. in Hebrew time gives the 
date of the vernal equinox = March 21.303,262, and of the full moon = March 
24.006,156. The difference 2.702,894 divided by 0.004,542,68 (the advance per 
year) gives 595 years before AD. 1883= AD. 12S8, when the full moon represented 
by GN. 1 coincided with the vernal equinox. Then to AD. 1238 add continually 
342.1 for the successive years of coincidence of the successive GN., and for the 
corresponding GN., continue to add 11 or to subtract 8 until the original GN. is 
reproduced at 6500 years after its first date. Then set down in the table these 
years of coincidence, except for GN. 9 subtract 6500 years, since the date as found 
is its next year of coincidence. (64, MDT. Mosaic in A.) (AC. Note 37.) 

(66). Then for the year of change take the centurial year that is nearest to the 
year of coincidence, and this will not allow the earliest full moon when it becomes 
the earliest in the table, to fall as much as 6 hours before or after the vernal equi- 
nox. Jackson (V. 2, p. 19) says: "Rabbi Moses Maimonides says, the equinox 
must be on or before the 15th Nisan." This is here interpreted to signify, that the 
full moon of Nisan must be on or next after the vernal equinox, because by the 
present rule the 15th Nisan is the date of full moon. And this interpretation agrees 
with the dates by the present calendar, as connected with astronomic facts in AD. 
807. (10-12, 28- 33, 64, 65.) 

(67). The result shows that the full moon of HC. represented by GN. 9, passed 
into the month Zif in AD. 946, and by GN. 1 in AD. 1288, and by GN. 12 in AD. 
1630. And GN. 4 will follow in AD. 1972. (17, 28-33, 64, 116-123.) 

(68). HC. and HCM. Rule 7. " Subtract one from the year HC. and divide R 
by 4," to cut off the Julian leap year HC. 1 and divide the years into periods of 4, 

22 



HC. NOTES. 

•with the remainder 1, 2, or 3 common years counting 365 days. Then each 4 years 
contain 1461 days or 5 days more than even weeks, and 365 days are one day more 
than even weeks. These with the constant 4, and divided by the circle 7 will give 
the ferial for the 31st of July OS. Then the day of Aug. OS. being added and 
divided by the circle 7, will give the ferial for the day of Aug. OS. as found by 
Rule. 

((89). HC. and HCM. Bute 8 is the result of Rules 2, 6, 7. And the dates of 
Moled Tisri being found by progression, the whole can be proved by the result 
when the GISTD. of the original G-N. is obtained, since the character of the second, 
as obtained by progression, must be the same as the character of the first with the 
addition of the character of a cycle. And when finding the day of the month by 
Rule 6, the hours and scruples must be the same as found by Rule 2. And the 
ferial found by Rule 7 must be the same as the ferial found by Rule 2. So that the 
date of Moled Tisri can be proved in different ways. But either of the other quan- 
tities may be erroneous, without affecting any other. (57, 63, 72.) 

(TO). HC and HCM. Bute 9, is obtained from Rule 4. (47-53.) 

HC. Examples from AD. 1883 to AD. 1902. 

(71). This table has been compared with the more extended table given by Lindo, 
who says that his calculations have been examined by Airy, the Astronomer Royal, 
and found to be correct, and that the whole work is approved by distinguished 
Rabbis in England. There are the following differences, besides that this carries 
the dates one year further in order to prove the accuracy of the calculations. 
(157-163.) 

(72). In 1887 he gives the year 5648 as 354 instead of 353 days ; and in 1897 he 
gives the Moled Sept. 2 instead of Sept. 26. These are evidently misprints. 

(73.) At page 11 he says : "Note. "When the hours are more than 12, they are 
so many past noon as they exceed that number." And in this table he marks them 
accordingly " M " for Morning and "A" for Afternoon. But all other writers and 
calculation agree, that IS hours = noon. And when mean conjunction falls at noon 
or 18 hours, Ja&li (Rule 3) transfers the date to the next day. And his dates prove 
that he follows this rule, by giving the same dates as in this table for the 1st Tisri 
in 1885, 1892, 1898, 1897, 1901. This is simply a mistake as to what 18 hours sig- 
nifies. (2, 13-14, 132-134.) 

(74). He reduces the scruples to minutes and seconds and fractions. These 
modern measures of time are foreign to this calendar. They would require all the 
characters to be reduced to minutes and seconds and fractions when working in 
characters. This is unnecessary labor, since the only use of the fractions of days 
is to find days. 

(75). Columns 9, 10, 11, are here given to exemplify the Rules. They are not 
given by him, and were unnecessary for his purpose as a simple calendar of dates. 
And this table is so arranged, that all the quantities in Cols. 7 to 12 are in strict ac- 
cordance with the standard rules by characters. And from the quantities in Cois. 
10 and 12, all the dates of the holidays can be found by Rules 4 and 5 without ref- 
erence to any other calendar, and without a standard solar year, except that it is 
the 19th part of 235 lunations =365. 246,822 days. But after proving the date of 
Moled Tisri by the Julian dates in Col. 8 in connection with the Julian date in Col. 

23 



HC. NOTES. 

6, and then by the rules of HC, finding the Julian date of 1st Tisri in Col. 13, it is 
more simple to find the familiar dates in Julian time, by means of Eule 9, and the 
day of January in a tabular form in A. Rules 2-4. In the Churchman's Year Book 
for 1870, William Moore, Esq., gives Lindo's table. 

HCM. Example AD. 70. 

(76). The error of interpretation by HC. Rule 1, is explained in connection with 
the example, which proves that HCM. Rule 1 is demanded for ancient dates. And 
this gives an example of determining the embolismic years (2.2-26), as in the ex- 
amples AD. 26 to AD. 37 as follows. (77.) And mean full moon fell at Jerusalem 
at 8 hours 38 min. a.m. on April 14 AD. 70. 

Examples of HC. and HCM. from AD. 26 to AD. 37. 

(77). The first table gives the dates according to the present calendar (HC). The 
second table according to the Mosaic rule (HCM.), assuming that the lunar dates by 
HC. are precisely correct. Hence in both tables the dates of Moled Tisri are the 
same except that in AD. 26 and in AD. 37, HCM. makes the date of Moled Tisri one 
lunation later than HC. because HC. gives the full moon of Adar instead of the 
full moon of Nisan. Thus : The first table shows the date of the Moled=AD. 26. . 
Aug. 31 . . 19 . . 662. Hence full moon of JSTisan March 22 . . 9 . . 620. MD. (A) makes 
full moon AD. 23 March 22.438,004 and vernal equinox March 23.508,150. Hence 
the full moon of HC. fell 1.070,146 day before the vernal equinox and was the full 
moon of Adar. Then in AD. 37, the Moled Aug. 29 . . 23 . . 510, gives the full moon 
of Nisan March 20. .13. .468. Then MD. gives full moon March 20.598,108, and 
vernal equinox March 23.172,526. Therefore the full moon of HC fell 2.574,418 
days before the vernal equinox and was the full moon of Adar. And AD. 26=GjST. 
6, and AD. 37=GK 17. And in the first century AD, GN. 6 and 17 always gave 
the full moon of Adar, by the rules of HC. The change is produced by removing 
E from GIST. 6 to GK 5, and from GK 17 to GN. 16. '"This makes the Moled fall 
one lunation later in GX. 6 and 17, as shown in the example of AD. 70. In all the 
other years, the dates of the Moled are the same. But HC. uses Jach=18 hours, 
and HCM. makes Jach 10 hours to transfer the date to the next day. And HC 
uses A, G, B of HC Rule 3, while HCM. omits these transfers. Then HC. counts 
the holidays as beginning in the evening before noon of the dates found by rule, 
while HCM. counts them as beginning in the evening after noon of the dates found 
by rule. And this has an important bearing on the date of the Crucifixion. (14, 
17, 22^5, 76, 87, 88, 89, 164-179.) 

Date of the Crucifixion. 

(78). The Evangelists show that Christ had a special passover and instituted the 
Lord's Supper on Thursday evening, and was crucified about noon of Friday, when 
the general passover or "high day," "the passover" began on Friday evening in 
Roman account, but the beginning of the Sabbath in Hebrew account. Matt. xxvi. 
17, 18 ; xxvii. 15, 46, 62 ; Mark xiv. 1, 12-14 ; xv. 6, 25, 34, 42 ; Luke xxii. 1, 7-11 ; 
xxiii. 17, 54 ; John xiii. 1, 2 ; xviii. 28, 39 ; xix. 14, 31. Here St. Mark says : 
" After two days was the passover " (xiv. 1). This in the Roman mode of counting 
both extremes signifies one day as we count. And the day of crucifixion is called 

24 



HC. NOTES. 



PASSOVERS. 



*' paraskeue" in tne Greek Testament, while the Greeks now call Friday "para- 
skeue." The word signifies preparation, ordinarily for the Sabbath, but in this 
year it was also for the passover (John xix. 14, 81). 

(79). Six different years are assigned. Jarvis in his Chronological History of 
the Church (pp. 370-410) makes the date March 25, AD. 28 ; Clinton, AD. 29 ; 
Schaff's Bible Dictionary (p. 181), April 7, AD. 30 ; Hales, AD. 31 ; Scaliger, De 
Emendatione Temporum (p. 562), April 3, AD. 83 ; Ussher's Chronology (Y. 10, 
pp. 555-562), April 3, AD. 33 ; Our Reference Bibles with Ussher's Chronology, 
AD. 33 ; John's Biblical Archaeology (p. 274), AD. 34. 

(§3). In the following table the numbers I. to VII. signify the evenings after 
noon of Sunday to Saturday upon which the passovers began according to the dif- 
ferent rules. " HC."=Hebrew Calendar by the present rules. "Mosaic" rules 
were still in force at these dates. And Nisan was at times "Postponed" to the 
next new moon by the Sanhedrim on account of the lateness of the crops. And 
HC. dates are one day earlier than found by rule, since HC. Rule 1 counts the 
dates as beginning in the evening before noon of the dates found by rule. (See 
Comparison of HC. and HCM. table.) (10-12, 22-26, 76.) (AC. Note 89.) 

(81). This table shows that AD. 33 is the only year 
among the above in which the passover began in the even- 
ing after noon of Friday. This is the date by the present 
rules and by the Mosaic rules, which differ in several re- 
spects, and two of them bear on the present question. 
First. HC. counts all Hebrew regular dates, one day 
earlier than the ancient rule which Maimonides believes 
to have been the Mosaic rule. (Thesaurus Antiquitatum 
Sacrarum, V. 17, p. 234.) HC. makes the regular date in 
AD. 33 to be Thursday. Second. In AD. 33 both rules 
make the new moon of Tisri fall Sept. 12, Day vii. .23 h. . 
533 scruples. Then both add one day because the hours 
are as much as 18 by HC. and 10 by HCM. This makes 
the 1st Tisri fall on Day i., where it is left by HCM. But by a rule of HC. which 
had no existence during the second temple, one day is added to prevent the 1st 
Tisri falling on Day i., iv., vi. Hence by the accidental counter-action of two de- 
partures from the ancient rule in AD. 33, HC. gives the Mosaic date. This is the 
year assigned by Scaliger and Ussher. And in this year, the Lord's Supper estab- 
lished in the evening after noon of Thursday, could not have been at the regular 
date of the passover. And such is the conclusion of Scaliger (pp. 567-574), and of 
Canon Farrar in his " Life of Christ" (V. 2, pp. 474-483). (10-12, 22-26, 34-45, 79.) 

(§2). But during the second temple, when dates were determined by the actual 
appearance of the new moon of Nisan, one day was added to the date if the moon 
was not actually seen on the day of its calculated appearance. This would add one 
day to the ferials in the 3d and 4th columns, and change V. to YI. only in AD. 
30, at the first moon, and in AD. 84 at the second moon. It is not probable that 
two unusual postponements occurred in the same year, so that the question rests 
between AD. 33 and AD. 30. Then to determine which of these two was the year, 
St. Mark (xiv. 12) shows that on Thursday sacrifices were made in the temple for 
the passover in the evening, while (xiv. 1) he says, "After two days was the pass- 
over." And St. John (xiii. 1) says of Thursday evening, at the time of the special 

25 









T3 


Q 






<D 


< 




p 


O 


u 




"c3 


& 


c5 


d 


m 
O 




28 


W 


3 
II. 


Si 


II. 


IY. 


29 


Yii. 


I. 


III. 


80 


IY. 


Y. 


YII. 


31 


II. 


III. 


IY. 


32 


II. 


II. 


III. 


33 


YI. 


YI. 


I. 


34 


II. 


III. 


Y. 



HC. NOTES. 

lassover, "Now before the feast of the passover." And (xix. 81), "for that Sab- 
oath day was a high day," i. e., " The passover," as St. Mark says (xiv. 1), begin- 
ning in the evening after noon of Friday. (11.) 

(§3). Now : Calculation shows no obvious reason for a special passover on the 
evening after noon of Thursday in AD. 33 when the general passover was on Fri- 
day evening, since Friday evening was the Mosaic date of the passover. But it 
does show that if AD. 80 was the year, then the Mosaic date of the passover was 
Thursday evening, and that the Sanhedrim must have postponed the date of the 
" high day,*' "The passover," to the next evening on account of clouds obscuring 
the new moon of Nisan on the day of its calculated appearance. This will account 
for the special passover on Thursday evening, because it was the Mosaic date of the 
passover. And since the sacrifices could only be killed in the temple, this shows 
that this was not the only special passover (Mark xiv. 12). Hence all the facts 
stated by the evangelists concur in AD. 80, and in neither of the other years And 
hence the conclusion that the crucifixion occurred about noon of Friday, April 7, 
AD. 80, and that the Lord's Supper was instituted at the Mosaic date of the Pass- 
over in the evening after noon of Thursday, April 6, AD 30. And this agrees with 
the date of the crucifixion in Schaff's Bible Dictionary (p. 181). (79, 164-179.) 

2d. Contra. Long (1253) says : "If the Jews had made use of the Julian year, 
and always kept their passover on the 14th of March, or if they had always kept 
it on the day of the astronomical full moon upon or next after the vernal equinox, 
as we can ascertain the time of our Lord's crucifixion within four or five years of 
the truth, we should then only have wanted to find out in which of those four or 
five years, the 14th March, or the before mentioned full moon was on Friday, and 
that would have characterized the very year ; but that was not the case. The Jew- 
ish year in our Saviour's time was irregular, as the beginning of it depended not 
upon the conjunction of the sun and moon, but upon the first appearance of the 
moon after conjunction, as settled by the Sanhedrim." Then the note : " de Judce- 
orum anno Christi sceculo, v. Petav. de doctrina temporum. Lib. 2, Cap. 27." 

3d. Mow: The evangelists do not mention the Roman date "the 14th March," 
(and that was too early for the Passover). But they do show that the Crucifixion 
occurred on Friday the 14th Nisan. And Maimonides shows that the 14th Nisan 
was the day of full moon. And Long and others show that the Sanhedrim post- 
poned the date one day when clouds obscured the new moon of Nisan, and to the 
next new moon when the crops were backward. But these irregularities are in- 
cluded in the above investigation, to prove that the Crucifixion could only have oc- 
curred in AD. 30 or 33 at the first moon, or AD. 34 at the second moon ; with the 
stronger reason to suppose that it was in AD. 30, on account of the double Pass- 
over. (164-168.) 

HCM. Table AD. 1883 to AD. 1902. 

(84). The only differences between this tableland the HC. Table arise from as- 
tronomic causes. In accordance with HCM. Rule 6, the embolismic years are G-N. 1, 
9, 12, instead of GN. 19, 8, 11 by HC. Rules 2, t 6. This makes the dates fall one 
lunation earlier in 1883, 1891, 1894, 1902, and substitutes the full moon of Nisan for 
the full moon of Zif. (57-59, 67, 71-75.) 

(§5). Then, by HCM. Rule 8, Jack transfers the date at 10 hours, instead of 18 
hours, to prevent the full moon falling later than the end of the 14th Nisan, when 

28 



HC. NOTES. 

the holiday is counted as beginning in the evening after noon of the date found by 
rule, as required by the Mosaic rule. (23-26, 76.) 

(§6). It so happens, that in this cycle, there is no case of Getrad or Betuthakpkat 
by HCM. Rule 3. In the HC. Table, Getrad occurs in 1886, when the character is 
iii . . 15 . . 1060, and the date is transferred at 18 hours by HC. Rule 3. But by HCM. 
Rule 3, Jach transfers the date at 10 hours, so that JA. in HCM. Table has the 
same effect as G in the HC. Table. And HCM. Rule 3, retains A, G, B, since 
each adds to the date, and therefore cannot bring the holiday earlier than was pos- 
sible under the ancient rule. And the ancient rule made the holiday fall later than 
its astronomic date, when the new moon of Nisan was not actually seen, although 
astronomically visible. (35-37, 41-45, 87-89.) 

General Remakes. 

(§7). " The Rev. Dr. Adler, Chief Rabbi of Great Britain," in a sermon copied 
into the Jewish Messenger, says : " Whoever is but slightly acquainted .... with 
the principles upon which the Hebrew calendar has been established, knows that 
at the time when the members of the great Sanhedrim were sitting at Jerusalem, 
the ocular observation of the new moon was indispensable, but the results of this 
were always checked by astronomical computation." (10-12, 144.) 

(§8). Also : " If at the present moment the temple should be restored, and the 
Sanhedrim re-established, the very same course as of old would be the only one 
that could be pursued, owing to the circumstance, that the fixing of the calendar 
depended entirely upon ocular observation of the new moon, and that calculation 
only was employed with a view to control that observation." (10-12, 144.) 

(89). Now, in such case the calendar would be nearly the same as HCM., but 
not precisely. HCM. assumes that the lunar date by HC. is precisely correct for 
all time. This is not precisely the fact. In AD. 607, HC. gave the lunar date 
3 minutes 4 seconds more than MD. And the HC. lunation is 5.42S8 seconds per 
year more than 29.530,589 days per lunation. This makes the lunar date in AD. 33 
to be 55 m. .35 sec. less than by MD., and in AD. 1883 to be 1 h. .54 m. more than 
by MD. Then in a prearranged calendar, the mean date is used, so as to vary as 
little as possible from the actual, which varies more than half a day more and less 
than the mean, and the actual would be used if dates were determined by actual 
observation. But as Sekles says : " Although at present there is a discrepancy of 
about 1 h. 43 m it answers all practical purposes, and is adopted in all coun- 
tries on the earth." (10, 14, 18, 87, 88, 154, 155.) 

Josephus' Dates. 

(90). Josephus in his Antiquities, which were published AD. 93, and in his "Wars 
of the Jews, which were published in AD. 75, gives his dates in terms of the Mace- 
donian months, which Scaliger says wer^ identical with the Roman months which 
he gives in a table, with the approximate Hebrew months. Whiston in his trans- 
lation, sometimes gives in brackets these approximate Hebrew months as explana- 
tory of the Macedonian months. In such cases the identical Roman month is here 
added to the approximate Hebrew month in the following. (52, 53, 112.) 

(91). Ant., Book 2, Chap. 4, Sec. 6 : '* God .... commanded Moses to tell the 
people .... that they should prepare themselves on the tenth day of the month 
Xanthicus against the 14th (which month is called by the Egyptians Pharmnthi, 

27 



HC. NOTES. 

and Nisan by the Hebrews ; but the Macedonians call it Xanthicus)." (10-12, 52, 
53, 93, 104-106, 108-412.) 

(92). A., B. 3, C. 10, S. 5 : "In the month Xanthicus, which is by us called 
Nisan, and is the beginning of our year, in the 14th day of the lunar month when 
the sun was in Aries .... was called the Passover." (91, 106.) 

(93). «A., B. 11, C. 4, S. 8 : " And as the feast of unleavened bread was at hand 
in the first month, which according to the Macedonians is called Xanthicus, but 

according to us Nisan And they offered the sacrifice which is called The 

Passover in the 14th day of the same month." (91.) 

(94). "Wars of frhe Jews, with respect to the siege and capture of Jerusalem by 
Titus in AD. 70. He gives these dates. 

(95). B. 5, C. 3, S. 1 : "On the feast of unleavened bread it being the 14th 

day of the month Xanthicus [Nisan" — April] ... " Eleazar opened the temple, 

and admitted such of the people as were desirous to worship God." (91, 93.) 

(96). B. 5, C. 7, S. 2 : "And thus did the Romans get possession of this first 
wall on the 15th day of the siege, which was the 7th of the month Artemisius 
[Iyar"-May] (107.) 

(97). B. 5, C. 13, S. 7: "In the interval between the 14th day of the month 
Xanthicus [Nisan "—April] "when the Romans pitched their camp about the city, 
and the first day of the month Panemus [Tamuz " — July]. (104, 105.) 

(9§). B. 6, C. 5, S. 3 : " When the people were come in great crowds to the 
feast of unleavened bread on the 8th day of the month Xanthicus [Nisan " — 
April]. This was on a former occasion, and Whiston in a note says that it was a 
week before the Passover, to purify themselves. (91, 93, 95, 108-110.) 

(99). B. 6, C. 8, S. 4: "And now were the banks finished on the 7th day of 
the month Gorpiceus [Elul" — September] "in 18 days' time." 

(100). B. 6, C. 8, S. 5 : "And as all was burning came that 8th day of the 
month Gorpiceus [Elul" — September] "upon Jerusalem." (103.) 

(101). B. 6, C. 9, S. 3 : " The greater part . . .were indeed of the same notion, 
come up from all the country to the feast of unleavened bread, and were on a 
sudden shut up by an army." Then to show the number of those who were prob- 
ably there, he says that on a former occasion : " When the high-priest upon the 
coming of the feast that is called the Passover, when they slay their sacrifices from 
the 9th hour till the 11th" — from the number of the sacrifices estimated that there 
were : — "2,700,200 persons that were pure and holy" — besides a vast number who 
were not. (10, 104.) 

(102). B. 6, C. 9, S. 4: "Now this vast number is indeed collected out of re- 
mote places, but the entire nation was now shut up as in a prison, and the Roman 
army encompassed the city when it was crowded with inhabitants." (96, 97.) 

(103). B. 6, C. 11, S. 1 : "And thus was Jerusalem taken in the second year of 
"Vespasian, on the 8th day of Gorpiceus [Elul" — September]. " It had been taken 

live times before, though this was the second time of its desolation And from 

King David to this destruction under Titus was 1179 years And thus ended 

the siege of Jerusalem." (100.) 

Conclusion from Josephtjs. 
(104). The Passover always begins in the evening at the end of the 14th Nisan 
(Ex. xii. 3-6). That which the Mosaic law requires to be done on the 14th Nisan, 

28 



HC. NOTES. 

Josephus in four places says was done on the 14th Xanthicus. (Ant., B. 2, C. 4, 
S. 6 ; B. 3, C. 10, S. 5 ; B. 11, C. 4, S. 8. Wars, B. 5, C. 3, S. 1.) And it was on 
this 14th Xanthicus AD. 70, that Eleazar admitted the people into the temple 
(Wars, B. 5, C. 3, S. 1), and when "the Romans pitched their camp by the city" 
(Wars, B. 5, C. 13, S. 7). (10-12, 25, 26, 76, 91-97.) 

(105). And this 14th Xanthicus was the 14th April, AD. 70, according to 
Muler, who (Chap, vii.) says that Josephus says that the Passover fell on April 
14, i. <?., in the evening of April 14. And this is the signification of the 14th 
Xanthicus according to Scaliger. Therefore in AD. 70, noon of April 14 was noon 
of the 14th Nisan. (25, 26, 53, 76, 127-130.) 

(106). Again. Ant., B. 3, C. 10, S. 5 : " in the 14th day of the lunar month 

when the sun was in Aries was called the Passover." This agrees with what 

is stated by others respecting the Mosaic rule. The sun enters Aries at the time of 
the vernal equinox and remains in Aries a little more than 30 days. So that the 
Passover always falls on the 14th day of the lunar month in the evening (Ex. xii. 
3-6) when the sun is in Aries. (10-17, 92, 115.) 

Indefinite dates by Josephus. 

(107). Wars, B. 5, C. 13, S. 7 and B. 5, C. 7, S. 2. The siege doubtless began 
on the 14th Xanthicus (April). The 15th day of the siege could not be the 7th 
Artemisius. This is probably the error of a copyist. The chances are in favor of 
the accuracy of the date 7th Artemisius. (96, 97, 112.) 

(108). Again. Antiquities, B. 2, C. 4, S. 6 : " God commanded Moses to tell 
the people. . . .that they should prepare themselves on the tenth day of the month 
Xanthicus against the 14th (which month is called by the Egyptians Pharmuthi, 
and Nisan by the Hebrews, but the Macedonians call it Xanthicus)." (10-12, 52, 
53, 91, 111, 112.) 

(109). This is evidently intended to be an explanation of the date of the Hebrew 
Passover in terms that were used by the Greeks at the time that Josephus was 
writing. But his explanation requires an explanation thus : Xanthicus is the Greek 
name of the Roman month April. They were identically the same. In AD. 70 
the siege of Jerusalem began on the 14th day of Xanthicus, and the same day was 
the 14th day of Nisan, that being the date of the full moon of Nisan, or full moon 
that fell on or next after the vernal equinox which in that year fell on March 22. 
The 14th Xanthicus was always the 14th April. But the 14th Nisan was the 14th 
April in AD. 70, only by accident. It fell each year about eleven days earlier 
until this would bring it earlier than March 22, the date of the vernal equinox, 
and then 30 days were added to this date. This was the average, so that the 
14th Nisan vibrated between March 22 and Xanthicus 19. (10-12, 52, 53, 71-75, 
104-105.) 

(110). Josephus does not intend to say that " God commanded Moses to tell the 
^people . . . that they should prepare themselves on the tenth day of the month 
Xanthicus for the 14th," as a standing rule. This Greek name for a Roman 
month was unknown in the time of Moses, and this would have made the 14th Ni- 
san, a purely solar date without regard to the moon. But he does mean that the 
14th Nisan should have the same relation to the sun and moon as the 14th Xanthi- 
cus in the year of the siege, or 19 years before or after. And that he does not 
-specify. 



HC. NOTES. 

(111). As to Pharmuthi. He does not explain whether he means the Old Style 
or the New Style of the Egyptian year in the Actian Era (AE.) His Antiquities 
were published AD. 93=AE. 122 ; and Censorinus wrote 145 years later in AE. 
267. He states among other dates to define that year, that the first day of Thoth 
fell on June 25th. This shows that Censorinus used the Old Style, and his readers 
would understand Pharmuthi, as used by Josephus, to begin on Feb. 26, in the year 
when his Antiquities were published. But the remark of Josephus, implying that 
Xanthicus and Pharmuthi were the same, shows that he intended his readers to 
understand that he uses the new style of the Actian Era, since that makes Phar- 
muthi always begin on March 27, so that the 14th Xanthicus was always the 14th 
April and the 19th Pharmuthi, but it was the 14th Nisan only once in 19 years, at 
the least. The old style of the Actian Era (AE.) only changed the number of the 
year so as to begin with JP. 4685. But it retained the canicular year of the Era of 
Nabonassar (NE.) with its 5 epagomenai, making the year always 365 days. So 
that in Julian time the dates receded one day in four years. The new style retain 
the regular 12 months of 30 days and 5 epagomenai of NE. in common Roman 
years. But in a Roman Bissextile it had 6 epagomenai, so that the First day of 
Thoth (New Year) always fell on the Roman Aug. 29. (112, 113, 140-145, 147, 
150, 152-156.) 

Contradictions. 

(112). As to Macedonian months. Whiston in brackets gives the equivalents, 
Xanthicus [Nisan] ; Artemisius [Iyar] ; Panemus [Tamuz] ; Gorpioeus [Elul]. 
These are the same as given by Scaliger, but with this difference. Whiston in his 
appendix gives the Hebrew names and the Macedonian names, and then the two 
Roman months in which the Hebrew months fall, as if the Hebrew and Macedon- 
ian months are the same. On the contrary, Scaliger says that the Macedonian and 
Roman months are identical, so that the Hebrew names are only approximations. 
And Muler says that Xanthicus is April. And the Greek use of Roman months 
under Greek names is analogous to the Egyptian use of their own names in the 
Actian Era (AE.), when, after their conquest, the year was changed to agree with 
the Roman year. It would be remarkable if the Greeks changed their year to 
agree with the Hebrew year. (52-53, 95-103.) 

(113). As to Pharmuthi and Xanthicus. McClintock and Strong (Month) say 
that — "Josephus synchronizes Nisan with the Egyptian Pharmuthi, which com- 
ncnnced March 27, and with the Macedonian Xanthicus, which answers generally 
to the early part of April."— Now, Josephus (Ant. B. 2, C. 4, S. 6) does not say that 
Pharmuthi commenced March 27. The inference is probably correct. Then ac- 
cording to Whiston — "The Macedonian Xanthicus answers generally to the early 
part of April." But Scaliger says that it is the Macedonian name of the Roman 
month April. (52, 53, 91, 111, 112.) 

(114). As to the double passover in the year of the Crucifixion Scaliger (pp. 567- 
574), and Canon Farrar in his Life of Christ (Y. 2, pp. 474-483), reach the conclu- 
sion that the Lord's Supper was not established at the regular date of the passover. 
Scaliger (p. 562), and Ussher (V. 10, pp. 555-562), make the date of the crucifixion 
April 3, AD. 33. Then (p. 555) Ussher says, " But in the first day of unleavened 
bread, when the passover was sacrificed (on 2d April) the disciples were sent." He 
then narrates the occurrences and the crucifixion. Then (p. 565), "that the bodies 
might not remain on the cross on the Sabbath day . . . (for that Sabbath was a 

30 



HC. NOTES. 

Great day)." This appears to imply that the sacrifices, "on April 2d," were for 
the passover in the evening of April 3d. But the Evangelists show distinctly that 
in the year of the crucifixion there was a passover on Thursday evening, while the 
"great day," "the High day," "the passover," i. e., the general passover, was on 
Friday evening. For this double passover there was no obvious reason, if the date 
of the crucifixion was April 3, AD. 33. But there was an obvious reason if the 
date was Friday, April 7, AD. 30, because the Mosaic date of the passover was in 
the evening of Thursday, April 6, AD. 30. The ancient rule removes the diffi- 
culty. (77-83, 164-179.) 

(115). As to the Seasons. Ideler is quoted by McClintock and Strong (Month) 
thus : " So much is certain that in the time of Moses, the month of ears [Abib or 
Nisan] cannot have commenced before the first of April, which was then the pe- 
riod of the vernal equinox." This appears to imply that the equinoxial date of the 
"Month of Ears" differed in different ages. Now, the exodus occurred JP. 3223, 
when MD. (A.) makes the vernal equinox fall April 3d. But Nisan never began 
less than 13 days before to 17 days after the vernal equinox. And this is an arti- 
ficial date which had no existence. Since that time the precession of the equinoxes, 
which carries the equinoxial points westward among the stars at the rate of about 
the semi-diameter of the sun in 19 years, has carried the equinoxial points about 
one-eighth of a circle westward. But this has no effect upon the seasons, which 
count from the time that the sun reaches the equinoxial point in the spring. And 
according to the ancient rule, which Maimonides believes to have been the Mosaic 
rule, the 1st Nisan began in the evening after the first appearance of the New 
Moon, which would bring the full moon of Msan on, or next after the vernal 
equinox. (106, 142.) 

(116). As to the Solar Error of HC. McClintock and Strong (Calendar) say : 
" The Jewish months, however, have been placed one lunation later than the rab- 
binical comparison of them with the modern Julian months, in accordance with 
the conclusions of J. D. Michaelis, published by the Royal Society of Goettingen. 
See Month." This appears to imply that the whole series of 19 GN. are a lunation 
too late. But at the present time (AD. 1639 to AD. 1939) all the GND. give Mo- 
saic dates, except the GND. of GN. 1, 9, 12. (67, 76, 77, 137.) 

(117). And under " Month" they continue to state the conclusions of Michaelis 
thus : " That the later Jews fell into this departure from their ancient calendar 
through some mistake in their intercalation, or because they wished to imitate the 
Romans, whose year began in March." 

(118). Now: There is no foundation for either of these suppositions. The 
present calendar appears to have been constructed on the basis of the solar and 
lunar dates in AD. 607, and about that time the solar dates corresponded precisely 
with the ancient rule. But in the first century AD., the GND. of GN. 6, 17, made 
the passovers fall one lunation too early. At the present time (AD. 1639 to AD. 
1939) the GND. of G$\ 1, 9, 12, make the passovers fall one lunation too late foi 
the ancient rule. And all the rest will follow at the rate of one passover in each 
342.1 years. (13-17, 30, 64-67, 119, 120, 122, 123, 137.) 

(119). But "this departure from their ancient calendar" is not, "through some 
mistake in their intercalation," as an accidental matter. Like all other ancient cal- 
endars (AM., JE., NC, OE., OS.), this assumes that 235 lunations are exactly 
equal to 19 equinoxial years. Like them, it has nothing analogous to NS. Table 

31 



HC. NOTES. 

II. ; AC. Table II. ; HCM. Rules 2 and 6, to follow each 235 the moon in its ad- 
vance from the vernal equinox for 6500 years, until it passes the limit of one luna- 
tion after the vernal equinox, and then to substitute a moon one lunation earlier. 
But, in consequence of the wonderful accuracy of the lunar dates, the true date 
of each moon will be given very nearly for all time, whether it be the full moon of 
Adar or of Zif, in place of the full moon of Nisan. (118, 119.) 

(120). For a similar reason, the Russo-Greeks (AM.) held Easter five weeks too 
late for the Nicean rule in AD. 1864. And the ecclesiastical date of their full moon 
of Nisan was five days after the date of the full moon of Zif (NB., AM.). (14, 
119, 131.) 

(121). As to "imitating the Bomans, whose year began in March." There is no 
apparent connection between the Hebrew and the Roman year, except that by the 
present rules, the 1st Tisri which falls in September and October, determines all 
the dates in that Roman year, but in two Hebrew years. And at present the year 
does not begin with March. And the Roman year is exclusively solar, and as 
nearly as practicable by whole numbers, the same Roman date represents the same 
equinoxial date with 12 months in three years of 365 and one of 366 days. On the 
contrary, the Hebrew year is exclusively lunar, and on the average recedes in equi- 
noxial date 11 days per year until it reaches the limit and then begins a lunation 
later, to recede again, and consists of 383, 384, 385 days when it has 13 months, and 
353, 354, 355 days when it has 12 months. And finally, it is intended to represent, 
and in AD. 607 it did (on this point) represent the rule established by Moses, before 
the Romans were in existence. (1, 10-14, 27-29, 40-42, 49, 71-83, 109, 139, 144.) 

(122). As to the Solar Error of HC. Professor Nesselman (Crelle, of 1844, p. 
179) says that the Jews are wrong in their rule, since — " In the embolismic years 8, 

11, 19, the Passovers will at times fall on the second and not on the first moon." 
He is answered : — " The object is to put the Passovers, not before the first, nor 
after the second." 

(123). Now: The dates of Moled Tisri in GN. 1, 9, 12 determine the dates of 
the previous Passovers. And by the present calendar, these "fall on the second 
moon," not only " at times," but always. And by the present interpretation, the 
Passovers always fall ' ' on " the date of full moon. And that was impossible under 
the Mosaic rule. Then the answer is partially correct, for the Mosaic rule admit- 
ted a postponement to the second moon. But that was only in emergencies while 
these are always. And at the present time only in the years preceding GN. 1, 9, 

12, and not in the remaining sixteen years of the cycle. But in the course of time 
the present calendar will put all the Passovers, not only "after the second," but 
after any number of full moons after the second. (10-14, 24, 64-67, 116-121.) 

(124.) As to the ZQ-day month of the Deluge. McClintock and Strong (Month) 
say : " We have therefore in this instance, an approximation to the solar month." 
On the contrary, these were Egyptian months, and neither solar nor lunar. (140- 
144, 151-153, 156.) 

(125). As to the date of HC. Different authors assign the following years as the 
date of construction of the present calendar, viz.: AD. 325, 345, 352, 353, 360, 369, 
424, 500, 525. But internal evidence indicates that it was constructed on the basis 
of astronomic facts in AD. 607. In that year the lunar date agrees with MDB. 
with a difference of only 3 minutes 4 seconds. This is slight evidence, since the 
lunar dates at all times are so nearly correct that they are assumed to be perfect. 

32 



HC. NOTES. 

But in AD. 607, this calendar makes the date of Moled Tisri Aug. 28. .16 hours 
exactly, and there is only one chance in 1080, that the date should by accident fall 
at two-thirds of a day without the difference of a single scruple. (1, 15-17, 
29, 30.) 

(126). Then as to the solar date. In the first century the dates of GN. 6 and 
GN. 17 bring the corresponding Passovers in the month Adar. At the present 
time the dates of GIST. 1, 9, 12 bring the corresponding Passovers in the month Zif. 
But in AD. 607 this calendar gave Mosaic dates with great precision. The ear- 
liest GN. is GN. 17, and AD. 607 being GN. 17, the vernal equinox fell March 
19.235,646; and the mean full moon fell March 19.250,558 according to MDB. The 
minute difference of 0.014,912, may be due to different standards for the date of 
the moon. But practically the dates are identical. And from AD. 607, the solar 
date of HC, separates from mean equinoxial date at the rate of 6 minutes 38 sec- 
onds per year, or the difference between a mean year of 365.242,216 and the HC. 
year of 365.246,822 days, or the 19th part of 235 lunations of 29 d . .12 h. .793 scru- 
ples. (11, 16, 17, 28-31, 57-67, 76.) 

(12T). As to the prime meridian of HC. Muler (Chap, vii.) calculates substan- 
tially thus : " Josephus says that in AD. 70, the Passover fell on April 14. Then 
add 163 days makes 1st Tisri=Sept. 24, AD. 70= JP. 4783. By rule of Ptolemy 
full moon fell JP. 4783 April 14. .4 h. .57. .34 from midnight under the meridian 
of Frisia. Add 8 h. .47. .10 [for longitude and to count from the previous 6 p.m.] 
=April 14. .13 h. .44. .44=April 14. .13. .805 [Hebrew time]=date of full moon 
at Eden in Babylonia [849 helakim (scruples) =1 h..23 m. east of Jerusalem] 
counting the hours from sunset. Then by rules of HC. New Moon of Nisan has 
the character vi. .19. .409, add half a month 0. .18. .396= vii. .13. .805 as before. 
The character of the New Moon of Nisan is derived from the following New 
Moon of Tisri which was i. .23. .847. Take for 6 months ii. .4. .438 and vi. .19. . 
409 remains." 

(12§). Now : This date is indefinite. Muler does not specify whether noon of 
the 15th Nisan was noon of the 14th April, so that the Passover began in the 
evening of April 13, according to the present interpretation by HC. Rule 1, or 
whether the 14th Nisan began in the evening of April 13 and the Passover in the 
evening of April 14, according to the interpretation of HCM. Rule 1. Josephus 
shows that HCM. Rule 1 is correct. (22-26, 76.) 

(12S>). Also, in the above, Muler by the rules of HC. finds the date of full 
moon vii. .13. .805. And " by rule of Ptolemy" he finds the same date April 14. . 
13. .805 when Eden is taken as the prime meridian. And there is only one chance 
in 1080 that two independent rules should give the same date without the differ- 
ence of a single scruple. Hence the inference that he puts the prime meridian cf 
the present calendar, at "Eden in Babylonia 849 helakim [scruples] east of Jeru- 
salem," because the " rule of Ptolemy" requires that longitude to give the same 
date as the present calendar. 

(130). On the contrary, history shows that Jerusalem was the prime meridian 
during the second temple. And the lunar date in AD. 607 by the present calendar, 
makes Jerusalem the prime meridian, '* ith the difference of only 3 minutes 4 sec- 
onds, from a mean lunation of 29.530,589 days. (10-14, 16, 18, 30, 87, 88.) 

(131). As to the Mosaic date of Easter. Lindo, in his Introduction, says ■ " The 
Council of Nice ordered that Easter should not be held on the first day of the 

33 



HC. NOTES. 

Passover 'ne videantur Judaizare.' But in 1825 and 1903, both fell on the same 
day." Here Lindo errs as to the Nicean rule. The day to be avoided " ne cum 
Judceis conveniamus," as the Missal has it, is not "the first day of the Passover," 
but the 14th day of Nisan which is the anniversary of the Crucifixion, and Easter 
must be held on Sunday next thereafter. This date was annually calculated by 
Egyptian astronomers until the century after the Council of Mcea, when the Alex- 
andrian Canon or Mcean Calendar (NC.) was used as a substitute. This was 
replaced by the Chalcedonian Calendar (OS., AM.) And that by the Gregorian 
Calendar (NS.) to which Lindo refers. Now Easter and the first day of the Pass- 
over fall on the days of full moon April 3, 1825, and April 12, 1903. But by the 
Mosaic rule, full moon could not possibly fall later than the 14th Nisan, so that 
Lindo's calendar is in error, and the Christians held Easter on the Mosaic 14th 
Nisan, contrary to the Nicean rule. (AC. Notes.) (10-12, 87-88, 120, 125, 126.) 

(132). As to the signification of Jack. Lindo says : " When the hours are more 
than 12, they are so many past noon." And in his table he marks them accordingly 
" M " for Morning and "A" for Afternoon. And he says that his calculations 
have been examined b}' Airy, the astronomer, and his whole work has been approved 
by distinguished Rabbis in Great Britain. On the contrary, MD. (A) makes new 
moon count from 6 p.m. at Jerusalem with a difference of only 3 m. 4 sec. in AD. 
607 from the date of Moled Tisri. lience when Moled Tisri falls at 18 hours, 
mean conjunction falls at noon. And Maimonides says : " The month begins in 
the night when new moon appears." And Sekles says : " Noon is 18 hours accord- 
ing to Talmudical computation." And Muler says : " Jewish time counts from 6 
hours after noon." And Scaliger says : " Since Jews count from the beginning of 
the night 18 hours come to noon." But while Lindo mistakes the signification of 
Jach or 18 hours, and shows that mistake in his table, he uses Jach correctly and 
transfers the date to the next day, when Moled Tisri reaches 18 hours (or noon) by 
rule which he then transforms to 6 Afternoon. (2, 13, 14, 71-74, 132-134, 137.) 

(133). Also. Scaliger (p. 126) says : " Since Jews count from the beginning of 
the night, 18 hours come to noon. Thus when the day appears to have passed, 
six hours yet remain to the beginning of the night." Now, this is not the fact. 
The addition of one day for the date of 1st Tisri, when the Moled Tisri falls as 
late as 18 hours, does not make the " day appear to have passed," but simply shows 
that mean conjunction falls at noon. Then at the end of that day at 6 p.m., the 
new moon will be only 6 hours old, and that being too early for Tisri to begin, the 
date is transferred to the next day. This is obviously the intention of the unknown 
author of this calendar. But by misinterpretation, the 1st Tisri begins before con- 
junction, as much as the hours and scruples in the date of Moled Tisri, until it 
reaches 18 hours. And this misinterpretation obscures the signification of Jach. 
(10-14, 22-26, 34-36.) 

(134). Also. Muler (Col. 81) says : " Since 6 p.m. to the following noon arc 18 
hours, this appears to be a just cause for the transfer." This is substantially an 
admission that he does not know what Jach signifies, because at the same time he 
explains in detail the reasons for the other complicated transfers by HC. Rule 3. 
(26, 34-37, 41, 42, 125, 126, 132, 133.) 

(135). As to the perfection of HC. To the sermon of Rev. Dr. Adler, Chief 
Rabbi of Great Britain, is appended this note : " This calendar has been so admi- 
rably regulated, that it has excited the admiration of some of the most learned as- 

34 



HC. NOTES. 

tronomers and mathematicians. Scaliger, a distinguished savant, writes : . . . 
'There is nothing more perfect, nothing more exact than the Jewish calendar.'" 
(87, 88.) 

(136). This is true as to the lunar dates, which are said to have been framed by 
Rab. Ada (or Adda), who was born in Babylon, AD. 188. These can be used for 
astronomical purposes with the minute correction of less than five and a half sec- 
onds (5. 3402) per year. And this calendar stands alone in giving dates to the pre- 
cision of a single scruple of 3£ seconds. Consequently it counts every day as one. In 
this it resembles the Metonic Cycle, and the Mohammedan Cycle. But they count 
nothing less than whole days, while the Egyptian Cycle, now used by all Chris- 
tians, counts nothing less than whole days, and makes no difference for the extra 
day in a leap year, so that it is the least accurate of all cycles, but at the same time 
the most simple of all cycles. But this excellence of the Hebrew calendar cannot 
be claimed for the use that is made of these excellent lunar dates. And I am not 
aware that any one has made a critical astronomical examination of this calendar 
before the present, to determine how far this claim of perfection can be substan- 
tiated. (2, 8, 13-14.) 

(137). As to HCM. Rule 1, no one refers to the constant error of counting the 
holidays one day too early. (22-26.) As to HCM. Rule 2, Nesselrnan does not 
seem to know, that the solar errors are constant, and are increasing. (122-123.) 
And MichaeHs appears to be in a fog on this point. (116-121.) And no one else 
has been found who refers to them. As to HCM. Rule 3, Scaliger, Muler, and 
Lindo do not appear to know what Jach signifies, and Lindo, who is certainly in 
error, says that his calculations have been examined by Airy, the Astronomer 
Royal, and his work approved by distinguished Rabbis. (132-134.) And no one 
has undertaken to show the necessity for substituting 10 hours for Jach or 18 hours. 
(35-36.) As to HCM. Rule 6 (64-67), nothing analogous has been found except Ta- 
ble II. of the Gregorian Calendar (NS. Table II.). And that is astronomically false. 
(AC. Notes). (64-67.) 

(13§). These modifications by HCM. are absolutely required to determine an" 
cient dates, when those dates were determined by actual astronomical observation. 
The characteristics of the calendar are not changed. If the changes by HCM. Rules 
1, 2, 3, 6, were now made, the difference would hardly be observed, except by the 
mathematician. In like manner, AC. Table II., analogous to the table in HCM. 
Rule 6, has been substituted for NS. Table II. of the Gregorian Calendar to cor- 
rect the errors of that table, while retaining the simplicity of that calendar, with- 
out the necessity of following the complications of the present Hebrew Calendar. 
(6-7, 57-70.) 

History. 

(139). The Hebrew mode of dividing the year and counting time, as shown by 
the present calendar, appears to have been derived from the Babylonian year with 
which they became familiar during the captivity from BC. 607 to BC. 536, or from 
JP. 4107 to 4178. 

(140). It is not the same as Moses used when they left Egypt, since he counts 
by months of 30 days in his account of the Deluge, which lasted 150 days from the 
17th of the 2d Month to the 17th of the 7th Month (Ex. vii. 2, 4, 24). (48, 149.) 

(141). In the time of Augustus, the Egyptians used as the popular calendar, the 
'* Canicular year," or the "Wandering year," which is called " Thoth" by Newton, 

35 



HC. NOTES. 

and generally the Era of Nabonassar (NE.). Tliis consisted of 12 consecutive 
months of 80 days and 5 epagomenai. By order of Augustus a sixth epagomena .5 
was added in the same year as the Roman bissextile (AE.). But still the Egyptians 
continued to use the 12 consecutive months of 30 days, so that we may infer thai 
this was the popular calendar in the time of Moses. And hence that Moses con- 
tinued to use months of 30 days, to which the Hebrews had been so long accus- 
tomed in Egypt. (Ill, 113.) 

(142;. This Egyptian year was neither solar nor lunar, but containing invariably 
365 days, receded a full Julian year in 1460 Julian years. But in Egyptian time 
it receded a Canicular year in 1508 years, from the "Year of God," when Thoth 
1st (New Year) coincided with the Heliacal rising of Canicula — the Dog star, or 
its first appearance in the East before sunrise, to its return to the same sidereal pe- 
riod, including the precession of the equinoxes, which carries the equinoxial points 
Westward among the stars a full circle in about 25,000 years (NE.). 

(143). The establishment of the passover required a year that should be both 
lunar and solar, while the Egyptian year was neither, but the best calendar for 
recording astronomical phenomena, and for recording dates with precision. Hence 
these Mosaic months of 80 days could not have coincided with Egyptian months, 
and they were numbered, not named. And among the various Hebrew names, 
there is not one which resembles the Egyptian names in NE. and AE. (52, 111, 
113, 140.) 

(144). Hence the inference, that the Mosaic mode of determining the beginning 
of the year, was the same as during the second temple, and such is the opinion of 
Maimonides. And hence, that beginning the year in the evening after the first ap- 
pearance of New Moon, which would bring the full moon on the 14th day of the 
first month on the day of the vernal equinox, or within one lunation thereafter., 
they counted 30 days for each month, until the new moon of the next year, and 
put the days between the end of the last full month, and the next new moon in the 
place of the Egyptian epagomenai of five days. And during the second temple, 
they did not know at the beginning of the year how many days that year would 
contain, nor whether it would be a year of 12 months or of 13 months. (10-12, 
50, 143.) 

(145). Newton (Y. 5, p. 284) says that "Thoth," of the Egyptians (NE.) was 
taken to Babylon, JP. 3967. The earliest definite date of an eclipse is given 
in terms of NE. at Babylon, JP. 3993 (NE., Ex.). This was 114 years before the 
Captivity. But this was probably used only in recording astronomical phenomena, 
without making any change in the popular calendar. And such is the opinion of 
Scaliger (p. 431). It was not well suited for popular use, because neither solar nor 
lunar, while the present Hebrew calendar and the Olympic calendar (OE.) are the 
best forms of ancient calendars for popular use, because they depended on the 
phases of the moon and the position of the sun, which required no calculation, and 
were both lunar and solar, while the Egyptian year was neither. (27-83, 142.) 

(146). The Hebrew Calendar (HC.) bears a strong resemblance to the Olympic 
Calendar (OE.). They were both luni-solar. HC. makes the full moon, on or next 
after the vernal equinox, the standard for the Passovers. And this is determined 
by the date of new moon. And OE. makes the new moon on or next after the 
summer solstice the standard for the Olympian games at full moon on the 15th 
day of the first month. Both depend upon the date of new moon. Both have 

36 



HC. NOTES. 

years of 12 and 13 months. And both can be traced back to Babylon. Thus 

(10-12.) 

(147). In JP. 4282, Meton determined the date of the summer solstice as the 
basis of OE., in terms of the Era of Nabonassar (OE. ; NE. Ex.). This shows that 
he was familiar with the Babylonian mode of recording astronomical phenomena. 
Hence the inference that the popular Greek mode of dividing the year may have 
come from the same source. And from its similarity to the Hebrew mode, that 
this may have come from Babylon. (10-12, 50.) 

(148). Maimonides, Scaliger, and Muler, say that the hour was divided into 
1080 scruples, or chelakim, or helakim, by Chaldeans and Arabians as well as by 
Hebrews, because 1080 is divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12. This peculiarity 
of the Hebrews, resembles the peculiarity of the Babylonians. (1, 2, 7.) 

(149). Jahn (p. 112) says : "During the captivity, the Hebrews adopted the 
Babylonian names of their months. They were Nisan, Zif or Ziv, Sivan, Tammuz, 
Ab, Elul, Tishri, Bui, Kislev, Tebeth, Shebat, Adar. The first month here men- 
tioned — Nisan— was originally called Abib." Smith (p. 580) says : " Three of these 
were used before the captivity. Abib in which the Passover fell (Ex. xiii. 4 ; xxii. 
15 ; xxxv. 18 ; Deut. xvi. 1) and which was established as the first month in com- 
memoration of the Exodus (Ex. xii. 2). Zif the second month (1 Kings vi. l. T 37) ; 
Bui the 8th (1 Kings vi. 38) and Ethanim seventh (1 Kings viii. 2). In the second 
place we have the names which prevailed subsequently to the Babylonish captivity; 
of these the following seven appear in the Bible : Nisan the first, in which the 
Passover was held (Neh. ii. 1 ; Esth. iii. 7) ; Sivan the third (Esth. viii. 9) ; Elul, 
6th (Neb. vi. 15) ; Chislu, 9th (Neh. i. 1 ; Zech. vii. 1) ; Tebeth, 10th (Esth. ii. 16) ; 
Sebat, 11th (Zech. i. 7) ; and Adar, 12th (Esth. iii. 7). The names of the remaining 
five occur in the Talmud and other works. They were Iyar the second (Targum, 
2 Chron. xxx. 2), Tammuz the 4th, Ab the 5th, Tisri the 7th, and Marchesvan the 
8th. The name of the intercalary month was Yeadar, i. e., the additional Adar." 
(48, 52, 53.) 

(150). Now : We find the peculiarity of counting time by scruples of 3£ sec- 
onds also among the Babylonians. And the structure of the Hebrew Calendar 
closely resembling that of the Olympic Calendar (OE.), with the probability that 
OE. was derived from the Babylonians. That Moses counted in consecutive 
months of 30 days, which are only elsewhere known to have been used by Egyp- 
tians, while we know from the structure of the Egyptian year, that the Mosaic 
months of 30 days could not have remained the same as the Egyptian months. 
Hence, since no Egyptian name is applied to months that are known to be Egyp- 
tian in form, the inference is justified, that they were not so called, because the 
arrangement of the months was not the same, and that the Babylonian names were 
retained because the arrangement of the months was the same and that the present 
Hebrew Calendar is of Babylonian origin. (140-150.) 

(151). Contra. Jahn (p. Ill) says : " It is evident from the history of the Del- 
uge, an attempt was made to regulate the months by the motion of the sun, and to 
assign to each of them 30 days ; but it was nevertheless observed after 10 or 20 
years that there was still a defect of five days." Also, Cruden (Month) and Smith 
(Month) and McClintock and Strong (Month), call months of 30 days "solar 
months." 

(152). Now : We know that the Egyptians used consecutive months of 30 days, 

37 



HC. NOTES. 

that were neither solar nor lunar, but receded in equinoxial date one day in four 
years without regard to the sun or moon. And that this " Wandering- Year " had 
five epagomenai at the end of 12 months of 30 days, to complete the year of 365 
days. And this was no defect in the year, but it is just the number of days that 
Jahn says was a "defect," in some kind of a year which he does not specify. And 
" ten or twenty years" is a large margin to observe a defect of five days. And he 
does not say whether it was "five days" in each year or in the 10 or 20 years. 
And he does not inform us who discovered this defect, and when. It could 
only be about the time of Moses, and it is supposed that no such Mosaic state- 
ment can be found. (124, 140, 142, 144, 153.) 

(153). And it is not obvious what connection a month of 30 days has with the 
sun. Certainly not the Egyptian month of 30 days, for that paid no regard to sun 
or moon. The Julian year is a solar year, and the months might be called solar 
months, although in themselves having no other connection with the sun. But 
these months are not consecutive months of 30 days, but vary from 28 to 29, 
30 and 31 days. The nearest approximation to a solar period of 30 days is the dura- 
tion of the sun in each of the 12 signs of the Zodiac. But this is not a solar month 
and is not referred to as such by these authors. And while these five distinguished 
authors call months of 30 days " solar months," neither of them as far as observed 
has given the reason. Perhaps it is supposed to be obvious, that since they are 
not lunar months, they must necessarily be solar months. (140-142.) 

(154). Also : Seabury (p. 13) says of the Egyptian year (NE.): " That this year 
was in use among the Chaldeans and Egyptians, from whom Abraham and Moses 
received it, there seems to be abundant evidence. Though we should admit with 
Dean Prideaux (in opposition to Kepler and Archbishop Ussher) that the years of 
the Jews in Canaan were purely lunar, yet they were careful by intercalating the 
oionths, to adjust them to the solar standard." 

(155). Now : There is no room for doubt that Moses was familiar with this 
Egyptian year, since he had always been accustomed to it, and he uses months of 
30 days in describing the duration of the Deluge ; and these are only known in 
the Egyptian calendars, and are purely artificial, since there is nothing in nature 
to suggest months of 30 days, while the phases of the moon suggest the lunar 
month alternately 29 and 30 days. But according to Newton, this Egyptian mode 
of recording astronomic phenomena was not used in Babylon before JP. 3967, 
and this was 1075 years after the death of Abraham in JP. 2892, according to 
Ussher's Chronology (Gen. xxv. 7). And the institution of the Passover necessarily 
demanded a "solar standard," and that standard must have been established by 
Moses. But, who knows that : — " they were careful by intercalating the months," 
to do it in that particular mode ? On the contrary, this supposes a prearranged 
calendar like the present. It is more likely, that no artificial calendar determined 
the dates, and that they were determined by direct astronomic observation, as they 
were during the second Temple. Such is the opinion of Maimonides, and of Rab. 
Adler. (12, 87-89, 140-145.) 

(15©). Josephus (Antiquities, B. 1, C. 8, S. 2) says of Abraham, with respect to 
the Egyptians : " He communicated to them arithmetic, and delivered to them 
the science of astronomy ; for before Abraham came into Egypt they were unac- 
quainted with those parts of learning ; for that science came from the Chaldeans 
into Egypt, and from thence to the Greeks also." This is improbable. But we 

38 



HC. NOTES. 



know that the Egyptian astronomic year was taken to Babylon in JP. 3967, and 
that the records there taken, were reported by Ptolemy of Alexandria, through 
whom we now receive them. (NE.) (145, 155.) 

(157). Comparison of the 14th Msan 
by HCM. and HC. with the mean date 
of full moon counted from 6 hours be- 
fore midnight at Jerusalem, with luna- 
tions of 29.500,589 days. (AC. Notes 
89-93.) 

(158). 1st Col. gives the year AD. in 
which the full moon represented by the 
GM coincides with the mean date of the 
vernal equinox and becomes the full 
moon of Msan, and the moon one luna- 
tion later becomes the full moon of Zif . 

(15B). 4th Col. gives the mean date 
of full moon in Hebrew time, on the 
basis of a lunation of 29.530,589 days, 
while the two last columns are on the 
basis of Hebrew lunations of 29 days 12 
hours 793 scruples, or 0.442 of a second 
more. In AD. 607 the mean date was 
3 minutes 4 seconds more than the He- 
brew date. In AD. 1883 it was 1 hour. . 
53 m. .35 seconds, or 0.078,167 of a day 
less. So that to compare dates, this 
0.0ii8,lG7 must be added to the dates in 
the 4th Col. (13-17, 30, 31, 71-75, 89, 
136-138) 

(B60). 5th Col. HCM." dates, and 6th Col. HC. dates are copied from the HCM. 
and HC. Tables with these modifications. By HCM. Rule 1, the day is counted as 
beginning in the evening after noon of the date found by rule, while by HC. Rule 1, 
the clay is counted as beginning in the evening before noon of the date found by rule. 
Then for the astronomic date, in both cases, take the date one day less than in the 
table when A adds one day and show that change by marking the date with A in 
this table. And in 1836 subtract two days and mark the date with G. 

(161). The 5 th Col. shows that when the difference of 0.078,167 between the cal- 
culations by mean lunations and by Hebrew lunations is added to the mean dates 
in the 4th Col., the rules of HCM. invariably make the 14th Msan fall on the day 
of full moon. 

The 6th Col. shows that by HC. Rule 1, counting the day as beginning in the 
evening before noon of the date found by rule, the 14th Msan is invariably before 
the date of full moon. 

(162). Also that GM 1, 9, 12, give the dates of the full moons of Zif. And the 
dates opposite in the first column show when they became the moons of Zif, and 
the dates when all the other GM will giVe the moons of Zif. But GN. 6 and GN. 
17 give the moons of Msan, while for the same years the present Greek Calendar 

39 











% 








«* 


te of 
oon 

Time. 


O 

HI 

S3 
03 


b 

m 

S3 

a 






< 






00 


<u O 

o 




u 


S3 F-j u 




tH 


1288 


1 


1883 


24.01 


24 


52 


3683 


2 


1884 


41.90 


41 


40 


6077 


3 


1885 


31.27 


31 


30 


1972 


4 


1886 


50.17 


50 A 


48 G 


4367 


5 


1887 


39.54 


39 A 


38 A 


261 


6 


1888 


27.90 


27 


26 


2656 


7 


1889 


46.80 


46 A 


45 A 


5051 


8 


1890 


36.17 


36 


34 A 


946 


9 


1891 


25.53 


25 A 


53 


3340 


10 


1892 


43.43 


43 


42 


5735 


11 


1893 


32.80 


32 


31 


1630 


12 


1894 


22.17 


22 


50 


4025 


13 


1895 


41.06 


41 A 


39 


6419 


14 


1896 


29.43 


29 


28 


2314 


15 


1897 


48.33 


48 


47 


4709 


16 


1898 


37.70 


37 A 


36 A 


604 


17 


1899 


27.06 


27 A 


25 


2998 


18 


1900 


45.96 


46 


44 


5393 


19 


1901 


35.33 


35 


34 


1288 


1 


1902 


24.69 


24 A 


52 


3683 


2 


1903 


43.59 







HC. NOTES. 

gives the moons of Zif. Because from internal evidence this calendar is based on 
astronomic facts in AD. 607, while the Greek Calendar began in AD. 534 with the 
full moon of Zif of GN. 6, and then received the full moon of Zif of GN. 17 in 
AD. 604. 

(163). Also. By Rule 3, HCM. transfers the date when Moled Tisri falls at 10 
hours, while HC. transfers the date at 18 hours. This makes the date by HCM. 
one day later than by HC, when the Moled falls between 10 and 18 hours, as in 
1886, 1890, 1891, 1895, 1899, 1900, 1902 in the HC. Table. And the same in the 
HCM. Table, except 1891 and 1894 when HC. gives the moons of Zif. And this 
difference of a day for the difference of 10 and 18 hours, added to the difference of 
a day by interpretation in counting the day as beginning before conjunction, makes 
the 14th Nisan fall two days before the date of full moon as shown in 1886, 1890, 
1895, 1899, and in 1900 when 0.078,167 is added to the mean date. 

Date of the Crucifixion. — Institution of the Lord's Supper. 

(164). Proposition. The Crucifixion occurred about noon of Friday, April 7, 
AD. 30, between two passovers on consecutive evenings, which were both recog- 
nized as such by the Sanhedrim. And the Lord's Supper was instituted on Thurs- 
day evening, April 6, AD. 30, at the regular Mosaic date of the Passover. (78-83 ; 
173-179.) 

(165). Different authors assign six different years on and between AD. 28 and 
AD. 34. But AD. 30 is the only year in which astronomic calculation proves, 
that every historic statement inside and outside of the Bible agrees with every other 
historic statement. (79.) Thus : 

(166). BC. 4 is the latest year that can be assigned to the Nativity, according to 
Roman history. (Farrar's Life of Christ, Vol. 2, p. 450.) (JE. Note 10.) 

(167). AD. 27 was the year in which Christ was baptized, according to Ussher's 
Chronology and our Reference Bibles. This is 30 years after BC. 4. And at this 
time St. Luke (iii. 23) says : "Jesus himself began to be about thirty years of age." 

(1€§). The Crucifixion occurred about three years after "the Baptism. (Farrar, 
Vol. 2, p. 471.) This makes the year of Crucifixion about AD. 30. 

(169). AD. 30 is the only year among the above in which the Passover could 
have fallen on Thursday evening as stated by St. Mark (xiv. 12), who says : " And 
the first day of unleavened bread when they killed the passover, his disciples said 
unto him, Where wilt thou that we go and prepare that thou mayest eat the pass- 
over?" (82.) 

(170\ This shows that the Passover on Thursday evening was recognized by 
the Sanhedrim. And on this evening the Lord's Supper was instituted. And cal- 
culation shows that this was the Mosaic date of the Passover. Thus : 

(171). The present Hebrew calendar makes Moled Tisri fall AD. 30. .Sept. 16. . 
8 hours. .352 scruples, and consequently the full moon of Nisan AD. 30. .at 4 hours, 
17 minutes, 13 seconds after noon of Thursday, April 6. The Mosaic rule made the 
Passover fall in the evening after the full moon of Nisan. Hence the Mosaic date 
of the Passover fell on Thursday evening, April 6, AD. 30, when the Lord's Sup- 
per was instituted. (10-14 ; 20 ; 77.) 

40 



HC. NOTES. 

(172). Also, AD. 30 is the only year among the above, when the postponement 
on account of clouds could have brought the " high day " on Friday evening, as| 
stated by St. John (xix. 4), who says : ' ' And it was the preparation for the pass- 
over." And (xix. 31), " That the bodies should not remain on the cross on the| 
Sabbath day (for that Sabbath was a high day)." (11.) 

Contradictions. 

(ITS). AD. 33 is the only possible year, according to the present Hebrew calen- 
dar, which makes the Passover fall in the evening of Monday in AD. 28 ; Saturday 
in AD. 29 ; Wednesday in AD. 30 ; Monday in AD. 31 ; Monday in AD. 32 ; Fri- 
day in AD. 33 ; and Monday in AD. 34. (81.) 

(174). AD. 33 is the year given in our Reference Bibles, and in Fordyce's 
Chronology, and in Rees's Cyclopaedia (Chronology). And (by inference) in 
Clarke's Commentary on Matt. xxvi. 17. (79.) 

75). AD. 33 is the year, according to Ussher's Chronology (pp. 555-564), in 
which he paraphrases the statements made by the Evangelists, but does not under- 
take to prove that their statements harmonize. (79, 114.) 

(176). AD. 33 is the year, according to Farrar's Life of Christ (Yol. 2, pp. 575- 
583), and according to Scaliger, De Emendatione Temporum (pp. 569-574). In 
these pages they show that the Lord's Supper could not have been instituted at the 
regular date of the Passover in AD. 33. (81.) 

(177). AD. 33 is the year, according to a writer in the Edinburgh Review, who 
says : " One of the most urgent critical questions of the day, is that of the colla- 
tion of the first three Gospels with the fourth The first three Gospels speak 

distinctly of the eating of the Passover by Christ and His disciples before the Cru- 
cifixion But the fourth Gospel states that the Crucifixion took place before 

the Passover This is where the conflict now halts." 

(17§). Now : This " conflict " arises from the use of the modern astronomic rule 
to determine ancient dates. The present calendar makes the full moon of Nisan 
fall in the afternoon of Thursday, April 6, AD. 30 (less than an hour earlier than 
fey present computation). The modern rule makes the Passover begin in the 
evening before full moon. But the Mosaic rule made it fall in the evening after 
full moon. Hence in AD. 30 the present calendar makes the Passover begin in 
the evening of Wednesday, and that does not agree with any statement in the four 
Gospels. But the Mosaic rule made the regular date fall on Thursday evening, 
and that agrees with every historic fact related, both inside and outside of the 
Gospels. 

(179). Hence the astronomic conclusion, that in AD. 30 the Sanhedrim recog- 
nized the Passover on Thursday evening, April 6, because it was the Mosaic date 
of the Passover. But in consequence of clouds having obscured the new moon of 
Nisan, the Sanhedrim had been compelled to postpone the " consecration " of the 
New Year one day later than its astronomic date. This brought the 15th day of 
Nisan one day after the true Mosaic date of the Passover. And the general Pass- 
over, " The Passover," the " High Day," was on the " 15th day of Nisan," as de- 
termined by the Sanhedrim. The Mosaic law (Ex. xii. 3-6) made the Passover 
always begin at the beginning of the 15th day of the first month. (10-14, 22-26, 
136, 137, 164, 171.) (AC. Notes 6-11, 75-80.) (Preface.) 

41 



JE. 



* 



JE= Julian Era— -Julian Calendar, began with the Bissextile t 'E. 1=B0. 45=: 
JP. 4669 =NE. 704= AU. 709, on January 1st. 

JE. Rule 1. For JE. into JP. : For the year JP. add 4668 to the year JE. Then 
in JE. Table find the modern day of the month corresponding with the Roman 
name, except in JC.O, and then to convert a bissextile into a leap year put the inter- 
calary "Bissextum Kalendas Martii " between Feb. 24 and 25, and add one day to 
Feb. 25, 26, 27, 28. And to find JC.O, subtract one from the year JE. and divide 
R. by 4, and 2d R. if 0=JC.O. And except as JE. Rule 3. 

JE. Bide 2. For JP. into JE. subtract 4668 from the year JP. for the year JE. 
Then in JE. Table find the Roman name for the day of the month except in JC.O. 
Then count Feb. 26, 27, 28, 29 one day less and put the intercalary between Feb. 

24 and 25. And except as JE. Rule 3. 

Day, 

JE. Rule 3. For JE. Correction. If the year JE. or JP. be 
found in this table. Then to the date found by JE. Rule 1, add 
the number of days opposite to the year in the table from Feb. 

25 of that year to Feb. 25 of the next year in the table. And 
from the date found by JE. Rule 2, subtract the number of 
days. 



JE. Rule 4. For dates in the Proleptic Julian year from Oct. 
13 AU. 707 to Dec. 31 AU. 708. Count them the same as by 
JE. Rules 1 and 2. 

JE. Example. The Actian Era (AE.) began NE. 720 Thoth 
lst= JP. 4685 Aug. 30. Then (Rule 2) subtract 4668 leaves JE. 
17. And (Rule 3) subtract one day, leaves the date JE. 17 Aug. 
29 as counted by the Romans. (AE. 1st Ex.) (AC. Notes 24-28, 
81, 85 : AE. Rule 9.) 



JE. 
1 


JP. 


4669 


4 


4672 


5 


4673 


7 


4675 


9 


4677 


10 


4678 


16 


4684 


17 


4685 


19 


4687 


21 


4689 


22 


4690 


28 


4696 


29 


4697 


31 


4699 


33 


4701 


34 


4702 


37 


4705 


41 


4709 


45 


4713 ' 



* See NS. Preface. 



JE. 



JE. TABLE. 



JANUARY. 


FEBRUARY. 




J3 
-t-i 
P 
O 


to 
D 

s 

CSS 

a 

ffS 

S 
o 
« 



H 


5 



0* 


o5 


i 

03 

<o 

E? 

P 
GO 


p 


5 
p 
o 


00 

o> 

a 

p 

A3 

a 

o 








00 

Oh 


0) 


1 


i 


Kal 


i 


iii 


* 


A 


32 


1 


Kal 


ix 




29 


D 


2 


2 


iv 






29 


B 


33 


2 


iv 




xi 


28 


E 


3 


3 


iii 


ix 


xi 


28 


C 


34 


3 


iii 


xvii 


xix 


27 


F 


4 


4 


Prid 






27 


D 


35 


4 


Prid 


vi 


viii 


(25) 26 


G 


5 


5 


Non 


xvii 


xix 


(25) 26 


E 


36 


5 


Non 






25,24 


A 


6 


6 


viii 


vi 


viii 


25 


F 


37 


6 


viii 


xiv 


xvi 


23 


B 


7 


7 


vii 






24 


G 


38 


7 


vii 


iii 


V 


22 


C 


8 


8 


vi 


xiv 


xvi 


23 


A 


39 


8 


vi 






21 


D 


9 


9 


V 


iii 


V 


22 


B 


40 


9 


V 


xi 


xiii 


20 


E 


10 


10 


iv 






21 


C 


41 


10 


iv 




ii 


19 


F 


11 


11 


iii 


xi 


xiii 


20 


D 


42 


11 


iii 


xix 




18 


G 


12 


12 


Prid 




ii 


19 


E 


43 


12 


Prid 


viii 


X 


17 


A 


13 


13 


Idus 


xix 




18 


F 


44 


13 


Idus 






16 


B 


14 


14 


xix 


viii 


X 


17 


G 


45 


14 


xvi 


xvi 


xviii 


15 


C 


15 


15 


xviii 






16 


A 


46 


15 


XV 


V 


vii 


14 


D 


16 


16 


xvii 


xvi 


xviii 


15 


B 


47 


16 


xiv 






13 


E 


17 


17 


xvi 


v 


vii 


14 


C 


48 


17 


xiii 


xiii 


XV 


12 


F 


18 


18 


XV 






13 


D 


49 


18 


xii 


ii 


iv 


11 


G 


19 


19 


xiv 


xiii 


XV 


12 


E 


50 


19 


xi 






10 


A 


20 


20 


xiii 


ii 


iv 


11 


F 


51 


20 


X 


X 


xii 


9 


B 


21 


21 


xii 






10 


G 


52 


21 


ix 




i 


8 


C 


22 


22 


xi 


X 


xii 


9 


A 


53 


22 


viii 


xviii 




7 


D 


23 


23 


X 




i 


8 


B 


54 


23 


vii 


vii 


ix 


6 


E 


24 


24 


ix 


xviii 




7 


C 


55 


24 


vi 






5 


F 


25 


25 


viii 


vii 


ix 


6 


D 


56 


25 


v 


XV 


xvii 


4 


G 


26 


26 


vii 






5 


E 


57 


26 


iv 


iv 


vi 


3 


A 


27 


27 


vi 


XV 


xvii 


4 


F 


58 


27 


iii 






2 


B 


28 


28 


V 


iv 


vi 


3 


G 


59 


28 


Prid 


xii 


xiv 


1 


C 


29 


29 


iv. 






2 


A 
















30 


30 


iii 


xii 


xiv 


1 


B 
















31 


31 


Prid 


i 


iii 


* 


C 

















JE. 



MARCO 






APRIL. 






B* 

a 
t-s 


E 
O 


a 
a 

o 

P3 


•-a 


d 


'A 

03 
Ok 


O) 

>> 
C3 

B 

B 
vi 

D 


B 

C3 


+3 
B 
O 


tn 

a 

B 

a 
& 






o 
es 

a* 


E 

"3 

§ 
J/2 


60 


i 


Kal 


i 


iii 


* 


91 


1 


Kal 


ix 




29 


G 


01 


2 


vi 






29 


E 


92 


2 


iv 




xi 


28 


A 


62 


3 


V 


ix 


xi 


28 


F 


93 


8 


iii 


xvii 




27 


B 


63 


- 4 


iv 






27 


G 


94 


4 


Prid 


vi 


xix 


(25) 26 


C 


64 


5 


iii 


xvii 


xix 


26 


A 


95 


5 


Non 




viii 


25,24 


D 


65 


6 


Prid 


vi 


viii 


(25) 25 


B 


96 


6 


viii 


xiv 


xvi 


23 


E 


66 


7 


Non 






24 


C 


97 


7 


vii 


iii 


V 


22 


F 


67 


8 


viii 


xiv 


xvi 


23 


D 


98 


8 


vi 






21 


G 


68 


9 


vii 


iii 


V 


22 


E 


99 


9 


V 


xi 


xiii 


20 


A 


69 


10 


vi 






21 


F 


100 


10 


iv 




ii 


IS 


B 


70 


11 


V 


xi 


xiii 


20 


G 


101 


11 


iii 


xix 




18 


G 


71 


12 


iv 




ii 


19 


A 


102 


12 


Prid 


viii 


X 


17 


D 


72 


13 


iii 


xix 




18 


B 


103 


13 


Idus 






16 


E 


73 


14 


Prid 


viii 


X 


17 


C 


104 


14 


xviii 


xvi 


xviii 


15 


F 


74 


15 


Idus 






16 


D 


105 


15 


xvii 


V 


vii 


14 


G 


75 


16 


xvii 


xvi 


xviii 


15 


E 


106 


16 


xvi 






13 


A 


76 


17 


xvi 


V 


vii 


14 


F 


107 


17 


XV 


xiii 


XV 


12 


B 


77 


18 


XV 






13 


G 


108 


18 


xiv 


ii 


iv 


11 


C 


78 


19 


xiv 


xiii 


XV 


12 


A 


109 


19 


xiii 






10 


D 


79 


20 


xiii 


ii 


iv 


11 


B 


110 


20 


xii 


X 


xii 


9 


E 


80 


21 


xii 






10 


C 


111 


21 


xi 




i 


8 


F 


81 


22 


xi 


X 


xii 


9 


D 


112 


22 


X 


xviii 




7 


G, 


82 


23 


X 




i 


8 


E 


113 


23 


ix 


vii 


ix 


6 


A 


83 


24 


ix 


xviii 




7 


F 


114 


24 


viii 






5 


B 


84 


25 


viii 


vii 


ix 


6 


G 


115 


25 


vii 


XV 


xvii 


4 


C 


85 


26 


vii 






5 


A 


116 


26 


vi 


iv 


vi 


3 


D 


86 


27 


vi 


XV 


xvii 


4 


B 


117 


27 


V 






2 


E 


87 


28 


V 


iv 


vi 


3 


C 


118 


28 


iv 


xii 


xiv 


1 


F 


88 


29 


iv 






2 


D 


119 


29 


iii 


i 


iii 


* 


G 


89 


30 


iii 


xii 


xiv 


1 


E 


120 


30 


Prid 






29 


A 


90 


31 


Prid 


1 


iii 


* 


F 

















JE. 



MAY. 


JUNE. 


a 


JO 

p 

o 


i/J 

& 

03 

s 
g 
o 
8 


4 


ft 
O 


O 


S- 

<v 

P 
3 
00 


1-5 


p 
o 


a 

S 
o 


\4 


Q 


05 
O 


■+J 

o 

C3 
t3 
P 
3 
02 


121 


1 


Kal 


ix 


xi 


28 


B 


152 


1 


Kal 


xvii 




27 


E 


122 


2 


vi 






27 


C 


153 


2 


iv 


vi 


xi 2 


(25) 26 


F 


123 


3 


V 


xvii 


xix 


26 


D 


154 


3 


iii 




viii 


25,24 


G 


124 


4 


iv 


vi 


viii 


(25) 25 


E 


155 


4 


Prid 


xiv 


xvi 


23 


A 


125 


5 


iii 






24 


1 


156 


5 


Non 


iii 


V 


22 


B 


126 


6 


Prid 


xiv 


xvi 


23 


G 


157 


6 


viii 






21 


C 


127 


7 


Non 


iii 


V 


22 


A 


158 


7 


vii 


xi 


xiii 


20 


D 


128 


8 


viii 






21 


B 


159 


8 


vi 




ii 


19 


E 


129 


9 


vii 


xi 


xiii 


20 


C 


160 


9 


V 


xix 




18 


F 


130 


10 


vi 




ii 


19 


D 


161 


10 


iv 


viii 


X 


17 


G 


131 


11 


V 


xix 




18 


E 


162 


11 


iii 






16 


A 


132 


12 


iv 


viii 


X 


17 


F 


163 


12 


Prid 


xvi 


xviii 


15 


B 


133 


13 


iii 






16 


G 


164 


13 


Idus 


V 


vii 


14 


C 


134 


14 


Prid 


xvi 


xviii 


15 


A 


165 


14 


xviii 






13 


D 


135 


15 


Idus 


V 


vii 


14 


B 


166 


15 


xvii 


xiii 


xv 


12 


E 


136 


16 


xvii 






13 


C 


167 


16 


xvi 


ii 


iv 


11 


F 


137 


17 


xvi 


xiii 


XV 


12 


D 


168 


17 


XV 






10 


G 


138 


18 


XV 


ii 


iv 


11 


E 


169 


18 


xiv 


X 


xii 


9 


A 


139 


19 


xiv 






10 


F 


170 


19 


xiii 




i 


8 


B 


140 


20 


xiii 


X 


xii 


9 


G 


171 


20 


xii 


xviii 




7 


C 


141 


21 


xii 




i 


8 


A 


172 


21 


xi 


vii 


ix 


6 


D 


142 


22 


xi 


xviii 




7 


B 


173 


22 


X 






5 


E 


143 


23 


X 


vii 


ix 


6 


C 


174 


23 


ix 


xv 


xvii 


4 


F 


144 


24 


ix 






5 


D 


175 


24 


viii 


iv 


vi 


3 


G 


145 


25 


viii 


XV 


xvii 


4 


E 


176 


25 


vii 






2 


A 


It46 


26 


vii 


iv 


vi 


3 


F 


177 


26 


vi 


xii 


xiv 


1 


B 


147 


27 


vi 






2 


G 


178 


27 


V 


i 


iii 


* 


C 


148 


2S 


V 


xii 


xiv 


1 


A 


179 


28 


iv 






29 


D 


149 


29 


iv 


i 


iii 


# 


B 


180 


29 


iii 


ix 


xi 


28 


E 


150 


30 


iii 






29 


C 


181 


30 


Prid 






27 


F 


151 


•31 


Prid 


ix 


xi 


28 


D 

















JE. 



QUINTILIS afterwards JULY. 


SEXTILIS afterwards AUGUST. 






to 








| 






S 

03 

to 








'A 

s 

o 

Hi 


c 


1 
1 


a 

a 

o 


• to 

a 

M 

•"3 


to 

o 

to 


m 

"5 


03 

'a 

p 

J3 

G 


d 

03 


o 


a 

03 

a 

o 


to 

05 


to 

o 

d 

to 


go 

o 

03 

a, 


03 

a 

0G 


182 


Kal 


xvii 


xix 


26 


213 


1 


Kal 


vi 


viii 


25,24 


C 


183 


2 


vi 


vi 


viii 


(25) 25 


A 


214 


2 


iv 


xir 


xvi 


23 


D 


184 


3 


V 






24 


B 


215 


3 


iii 


iii 


V 


22 


E 


185 


4 


iv 


xiv 


xvi 


23 


C 


216 


4 


Prid 






21 


F 


186 


5 


iii 


iii 


V 


22 


D 


217 


5 


Non 


xi 


xiii 


20 


G 


187 


6 


Prid 






21 


E 


218 


6 


viii 




ii 


19 


A 


188 


7 


Noa 


xi 


xiii 


20 


F 


219 


7 


vii 


xix 




18 


B 


189 


8 


viii 




ii 


19 


G 


220 


8 


vi 


viii 


X 


17 


C 


190 


9 


vii 


xix 




18 


A 


221 


9 


V 






16 


D 


191 


10 


vi 


viii 


X 


17 


B 


222 


10 


iv 


xvi 


xviii 


15 


E 


192 


11 


V 






16 


C 


223 


11 


iii 


V 


vii 


14 


F 


193 


12 


iv 


xvi 


xviii 


15 


D 


224 


12 


Prid 






13 


G 


194 


13 


iii 


V 


vii 


14 


E 


225 


13 


Idus 


xiii 


XV 


12 


A 


195 


14 


Prid 






13 


F 


226 


14 


xix 


ii 


iv 


11 


B 


196 


15 


Idus 


xiii 


XV 


12 


G 


227 


15 


xviii 






10 


C 


197 


16 


xvii 


ii 


iv 


11 


A 


228 


16 


xvii 


X 


xii 


9 


D 


198 


17 


xvi 






10 


B 


229 


17 


xvi 




i 


8 


E 


199 


18 


XV 


X 


xii 


9 


C 


230 


18 


XV 


xviii 




7 


F 


<J00 


19 


xiv 




i 


8 


D 


231 


19 


xiv 


vii 


ix 


6 


G 


201 


20 


xiii 


xviii 




7 


E 


232 


20 


xiii 






5 


A 


202 


21 


xii 


vii 


ix 


6 


F 


233 


21 


xii 


XV 


xvii 


4 


B 


203 


22 


xi 






5 


G 


234 


22 


xi 


iv 


vi 


3 


C 


2J4 


23 


X 


XV 


xvii 


4 


A 


235 


23 


X 






2 


D 


205 


24 


ix 


iv 


vi 


3 


B 


236 


24 


ix 


xii 


xiv 


1 


£ 


206 


25 


viii 






2 


C 


237 


25 


viii 


i 


iii 


* 


F 


207 


26 


vii 


xii 


xiv 


1 


D 


238 


26 


vii 






29 


G 


208 


27 


vi 


i 


iii 


* 


E 


239 


27 


vi 


ix 


xi 


28 


A 


209 


28 


V 






29 


F 


240 


28 


V 




xix 


27 


B 


210 


29 


iv 


ix 


xi 


28 


G 


241 


29 


iv 


xvii 




26 


C 


211 


30 


iii 




xix 


27 


A 


242 


30 


iii 


vi 


viii 


(25) 25 


D 


212 


31 


Prid 


xvii 




(25)26 


B 


243 


31 


Prid 






24 


E 



JE. 



SEPTEMBER. 


OCTOBER. 






5 

P 
O 


a 

03 

a 

03 

s 

o 




6 


o 


53 

■+3 

oj 
e? 

F 


a 

S3 

274 


p 
o 

2 


a> 

B 

T3 

p 

03 

s 

o 




d 


.2 
o 

03 


33 

<V 

o? 

P 

S 


244 


i 


Kal 


xiv 


xvi 


23 


1 


Kal 


iii 


xvi 


22 


A 


245 


2 


iv 


iii 


V 


22 


G 


275 


2 


vi 




V 


21 


B 


246 


3 


iii 






21 


A 


276 


3 


V 


xi 


xiii 


20 


C 


247 


4 


Prid 


xi 


xiii 


20 


B 


277 


4 


iv 




ii 


19 


D 


248 


5 


Nod 




ii 


19 


C 


278 


5 


iii 


xix 




18 


E 


249 


6 


viii 


xix 




18 


D 


279 


6 


Prid 


viii 


X 


17 


F 


250 


7 


vii 


viii 


X 


17 


E 


280 


7 


Non 






16 


G 


251 


8 


vi 






16 


F 


281 


8 


viii 


xvi 


xviii 


15 


A 


252 


9 


V 


xvi 


xviii 


15 


G 


282 


9 


vii 


V 


vii 


14 


B 


253 


10 


iv 


V 


vii 


14 


A 


283 


10 


vi 






13 


C 


254 


11 


iii 






13 


B 


284 


11 


V 


xiii 


XV 


12 


D 


255 


12 


Prid 


xiii 


XV 


12 


C 


235 


12 


iv 


ii 


iv 


11 


E 


256. 


13 


Idus 


ii 


iv 


11 


D 


286 


13 


iii 






10 


F 


257 


14 


xviii 






10 


E 


287 


14 


Prid 


X 


xii 


9 


G 


258 


15 


xvii 


X 


xii 


9 


F 


288 


15 


Idu? 




i 


8 


A 


259 


16 


xvi 




i 


8 


G 


289 


16 


xvii 


xviii 




7 


B 


260 


17 


XV 


xviii 




7 


A 


290 


17 


xvi 


vii 


ix 


6 


C 


201 


18 


xiv 


vii 


ix 


6 


B 


291 


18 


XV 






5 


D 


262 


19 


xiii 






5 


C 


292 


19 


xiv 


XV 


xvii 


4 


E 


263 


20 


xii 


XV 


xvii 


4 


D 


293 


20 


xiii 


iv 


vi 


3 


F 


264 


21 


xi 


iv 


vi 


3 


E 


294 


21 


xii 






2 


G 


265 


22 


X 






2 


F 


295 


22 


xi 


xii 


xiv 


1 


A 


266 


23 


ix 


xii 


xiv 


1 


G 


296 


23 


X 


i 


iii 


* 


B 


267 


24 


viii 


i 


iii 


* 


A 


297 


24 


ix 






29 


C 


268 


25 


vii 






29 


B 


298 


25 


viii 


ix 


xi 


28 


D 


269 


26 


vi 


ix 


xi 


28 


C 


299 


26 


vii 




xix 


27 


E 


270 


27 


V 




xix 


27 


D 


300 


27 


vi 


xvii 




26 


F 


271 


23 


iv 


xvii 




(25) 26 


E 


301 


28 


V 


vi 


viii 


(25) 25 


G 


272 


29 


iii 


vi 


viii 


25,24 


F 


302 


29 


iv 






24 


A 


273 


30 


Prid 


xiv 




23 


G 


303 


30 


iii 


xiv 


xvi 


23 


B 
















3C4 


31 


Prid 


iii 


v 


22 


C 



JE. 



NOVEMBER. 


DECEMBER. 


p 
cs 


J3 

4-= 

p 
o 

* 


33 
<D 

B 

a 
p 

s 

o 

05 




O 

Q 
ft 


CO 

o 

C3 


to 

a> 

-4-2 

<D 

hJ 

>J 

S3 

"3 
P 
P 

02 

D 


a 

r-8 


.9 

p 
o 


to 

s 
& 

p 

C3 
P 

o 

PS 


•-a 




o 

a 


CO 

a> 

p 
p 

0Q 


305 


1 


Kal 






21 


335 


i 


Kal 


xi 


xiii 


20 j 


F 


306 


2 


iv 


xi 


xiii 


20 


E 


336 


2 


iv 




ii 


19 


G 


307 


3 


iii 




ii 


19 


F 


337 


3 


iii 


xix 




18 


A 


308 


4 


Prid 


xix 




18 


G 


338 


4 


Prid 


viii 


X 


17 


B 


309 


5 


Non 


viii 


X 


17 


A 


339 


5 


Non 






16 


C 


310 


6 


viii 






16 


B 


340 


6 


viii 


xvi 


xviii 


15 


D 


311 


7 


vii 


xvi 


xviii 


15 


C 


341 


7 


vii 


V 


vii 


14 


E 


312 


8 


vi 


V 


vii 


14 


D 


342 


8 


vi 






13 


F 


313 


9 


V 






13 


E 


343 


9 


V 


xiii 


XV 


12 


G 


314 


10 


iv 


xiii 


XV 


12 


F 


344 


10 


iv 


ii 


iv 


11 


A 


315 


11 


iii 


ii 


iv 


11 


G 


345 


11 


iii 






10 


B 


316 


12 


Prid 






10 


A 


346 


12 


Prid 


X 


xii 


9 


C 


317 


13 


Idus 


X 


xii 


9 


B 


347 


13 


Idus 




i 


8 


D 


318 


14 


xviii 




i 


8 


C 


348 


14 


xix 


xviii 




7 


E 


319 


15 


xvii 


xviii 




7 


D 


349 


15 


xviii 


vii 


ix 


6 


F 


320 


16 


xvi 


vii 


ix 


6 


E 


350 


16 


xvii 






5 


G 


321 


17 


XV 






5 


F 


351 


17 


xvi 


XV 


xvii 


4 


A 


322 


18 


xiv 


XV 


xvii 


4 


G 


352 


18 


XV 


iv 


vi 


3 


B 


323 


19 


xiii 


iv 


vi 


3 


A 


353 


19 


xiv 






2 


C 


324 


20 


xii 






2 


B 


354 


20 


xiii 


xii 


xiv 


1 


D 


325 


21 


xi 


xii 


xiv 


1 


C 


355 


21 


xii 


i 


iii 


* 


E 


326 


22 


X 


i 


iii 


* 


D 


356 


22 


xi 






29 


F 


327 


23 


ix 






29 


E 


357 


23 


X 


ix 


xi 


28 


G 


328 


24 


viii 


ix 


xi 


28 


F 


358 


24 


ix 




xix 


27 


A 


329 


25 


vii 




xix 


27 


G 


359 


25 


viii 


xvii 




26 


B 


330 


26 


vi 


xvii 




(25) 26 


A 


360 


26 


vii 


vi 


viii 


(25)25 


C 


331 


27 


V 


vi 


viii 


25,24 


B 


361 


27 


vi 






24 


D 


332 


28 


iv 






23 


C 


362 


28 


V 


xiv 


xvi 


23 


E 


333 


29 


iii 


xiv 


xvi 


22 


D 


363 


29 


iv 


iii 


V 


22 


F 


334 


30 


Prid 


iii 


V 


21 


E 


364 


30 


iii 






21 


G 
















365 


31 


Prid 


xi 


xiii 


(19)20 


A 



JE. NOTES. 

JE.= JULIAN ERA= JULIAN CALENDAR. 



1. As to JE. Bules 1 to 3. JE. 1=BC. 45 was a bissextile. Calculation assumes 
that JE. 1 and each 4th year before and after JE. 1 was a bissextile or a leap year. 
But through error, the Romans counted JE. 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 
as bissextiles, and corrected this error of 3 days, by omitting the regular intercal- 
aries in JE. 37, 41, and 45. So that after Feb. 24 in JE. 45 or BC. 1, the dates 
became regular. Rule 3 changes the irregular Roman dates into regular dates of 
calculation and the reverse. • This is shown in JE. Example, and more fully in 
AE. Note 9. 

2. As to JE. Rule 4. The last " year of confusion" was calculated backwards 
from Oct. 13 to Dec. 31 and contained 445 days, and was called the Proleptic 
Julian year. For an extended account of the Roman year, see Jarvis' Chronolog 
ical History of the Church, pp. 55-97. (AC. Notes 99-101.) 

3. As to JE. Table. The first Col. gives the day of January or day of the year 
in a common year of 365 days, as in Appendix (Jan. Min.). The 2d and 3d Col. 
the day of the month in the modern and in the Roman form. And the Roman 
intercalary Bis-sextum Kalendas Martii, was between Feb. 24 and 25, or the "sec- 
ond sixth before March 1st" in the Roman mode of counting both extremes. Then 
JE. GN= JE. Golden Numbers, are put opposite to the dates of new moon, count- 
ing JE. 1 or BC. 45 as GN. 1. Thus, history says that JE. began on Jan. 1, BC. 
45, on the day of new moon. And MD. makes new moon fall 7 h. 23 m. after 
noon at Rome in BC. 45. This is an Egyptian form of the cycle of 235 new moons 
in 19 years, which was adapted to Roman dates by Sosigenes, the Egyptian astron- 
omer, who framed the Julian Calendar. Then NC. GN. are the Nicean Calendar 
GN. or the GN. of the Alexandrian cycle, which was the first Christian calendar, 
and was adopted in the century after the Council of Nicea in AD. 825, to deter- 
mine the dates of Easter. This puts GN. 3 at March 31/ and MD. makes new 
moon fall at Jerusalem 1 hour 42 minutes a.m. of March 31, AD. 325. Con- 
sequently NC. GN. 3=AD. 325. And from that day to the present the Westerns 
have always counted AD. 325=GN. 3. But JE. GN. 9=AD. 325 which is put 
at April 1, or one day later. Because in Julian time the date of the moon recedes 
0.3241 day per century, and from BC. 45 to AD. 325 it had receded 1.19 day. 
(AC. Notes 101.) 

4. Jarvis (pp. 87-92) gives both of these Egyptian cycles, with remarks which 

8 



JE. NOTES. 

are criticised (AC. Notes 94-101). The characteristics of the Egyptian cycle are 
given in AC. Rules and Notes. 

5. The Roman Epacts were introduced in AD. 1582 and are copied from the 
Roman Missal, where they are given without the corresponding GN. But when 
in this table they are collated with these two Egyptian cycles, it appears that the 
standard Epact * is at the same date as JE. GN. 1 and NC. GN. 3 throughout 
the entire cycle. They are substantially dates of GN. in the reverse order. And 
they divide the year into lunar months of 30 and 29 days, as the Sunday letters 
divide the year into weeks of 7 days. So that the Epact for the year determines 
the Epact of the GN. instead of its date, as the dominical determines which day is 
Sunday. And the explanation in the Missal shows how the Epacts are obtained 
from the GN. Contra (AC. Notes 120-130). 

6. The Sunday letters A to G, are derived from the Roman Nundinal letters A 
to H in the Julian Calendar. 

History. 

(7). Anthon (Calendars) says that the introduction of JE. was postponed to the 
date of new moon, so that the lunar cycle might begin on the first day of the year, 
and that modern computation makes new moon fall JP. 4669, Jan. 1, at6h. 6 m. 
P.M. The JE. table shows GN. 1, at Jan. 1, and MD. makes the mean date of 
new moon JP. 4669, Jan. 1, at 7h. 23 m. P.M. (3.) 

(§). Brady (p. 27) says that originally February had 29 days in a common year, 
and Sextilis had 30 days. But when Augustus changed the name of Sextilis to 
August, he took one day from February and added it to August. Also (p. 26), on 
the restoration of Charles II., the revivers of the Liturgy changed the intercalary 
to Feb. 29. 

(9). AE. Note 9, shows that after the confusion of dates arising from putting the 
intercalaries in the wrong years, the first regular date was Feb. 25, BC. 1. And 
BC. 1 is the basic year of the Western lunar cycle, to find the ' ' Prime " or Golden 
Number. And this is the same as the original Egyptian cycle which was adopted 
in the fifth century AD., as the first Christian calendar. (AC. Notes 81-84.) 

(10). Also, the first perfect year after this confusion of dates, was AD. 1. This 
may have been intentional on the part of Dionysius when he proposed this year as 
the standard of the Dionysian Period. (HC. Notes 166-170.) 

(11). For the long and short months : Take the 4 fingers and 3 spaces. Then 
count Jan.=lst finger, Feb.=lst space, etc., to July=4th finger, Aug.=lst finger, 
etc., to Dec. = 3d finger. Then the fingers represent the long months, and the 
spaces the short months. Was this intentional ? 

(12). Contra. Adams (p. 355) says : " Ceesar was led to this method of regu- 
lating the } r ear, by observing the manner of computing time among the Egyptians, 
who divided the year into 12 months, each consisting of 30 days, and added 5 inter- 
calary days at the end of the year, and every fourth year, 6 days. Herodot. ii. 4. 
These supernumerary days Caesar disposed of among those months which now con- 
sist of 31 days, and also the two days which he took from February ; having ad- 
justed the year so exactly to the course of the sun, says Dio, that the insertion of 
one intercalary day in 1461 years, would make up the difference (Dio, xliii. 26), 
which, however, was found to be ten days less than the truth. Another difference 
between the Egyptian and Julian year was, that the former began in September, 
&nd the latter in January. 

9 



JE. NOTES. 

(IS). Now : Sosigenes, the author of the Julian Calendar, was an Egyptian 
astronomer. There can be no doubt that JE. with three years of 365 days, and a 
fourth with 366 days, was founded on the Egyptian year. But the table, AE. 
Note 9, shows : 

(14). First. JE. was established JP. 4669, and AE. was established JP. 4685. 
And until JP. 4685, the Egyptian year (NE.) had invariably 365 days, and hence 
in Julian time receded one day in each four years, and a full year in 1461 Egyp- 
tian years, or 1460 Julian years. 

(15). Second. In JP. 4685 the Egyptians were compelled by the conquering 
Romans to add the sixth intercalary in the same year as the Roman bissextile, so 
that instead of having a different Roman date every 4 years, the Egyptian year 
should always begin on August 29 in Roman time, and not in " September." (AE.) 

(16). Third. 1461 years required a full year, and not "one intercalary day," to 
" make up the difference " between the old Egyptian year and the Roman year. 
And in AD. 1582, the difference " was found to be ten days," that the Julian year 
was too long, and NS. eliminated these ten days by counting October 5, OS. = October 
15, NS., and thereafter excluding 3 intercalaries in 4 centuries. (AC. Notes 31-35 ; 
AE. Notes ; NS. Notes ; AU.) 

(17). Authors: Adams' Roman Antiquities (pp. 352-358) ; Brady's Clavis Calan- 
dria ; Jarvis' Chronological History of the Church (pp. 44-96) ; Long's Astronomy 
(Sec. 1241-1248) ; Anthon's Classical Dictionary (Calendars) ; Rees' Cyclopaedia 
(Calendar). 

10 



ME. 



ME.=MOHAMMEDAN ERA=TURKISH CALENDAR. 



These rules count from Thursday, July 15, AD. 622, in civil time from sunset 
after noon, and one day less than the same actual date, Friday, July 16, AD. 622, in 
Mohammedan time, from sunset before noon. 

ME. Rulel. Mohammedan Cycle of 30 years. 





GN. 


GND. 




GN. 


GND. 




GN. 


GND. 




GN. 


GND. 




1 







9 


2835 




17 


5670 




25 


8505 


K 


2 


354 


K 


10 


3189 


K 


18 


6024 


K 


26 


8859 




3 


709 




11 


3544 




19 


6379 




27 


9214 




4 


1083 




12 


3898 




20 


6733 




28 


9568 


K 


5 


1417 


K 


13 


4252 


K 


21 


7087 


K 


29 


9922 




6 


1772 




14 


4607 




22 


7442 




30 


10,277 


K 


7 


2126 




15 


4961 




23 


7796 




1 


10,631 




8 


2481 


K 


16 


5315 


K 


24 


8150 









ME. Rule 2. Distances of first days of the months from the beginning 
year. 



of the 



Moharrem (Muharrem, Mohurrum) , 

Saf ar (Safer, Saaf ar) , 

Rabi-el-awwel (el-aouel, el-ewwel, prior). . . 
Rabi-el-accher (el-akhir, el-thany, posterior). 
Dschemadi el-awwel (Djemasi, Djoumadi)., 
Dschemadi-el-accher (Djemasi, Djoumadi). . . 

Redscheb (Redjeb, Rajeb) 

Shaban (Saban, Chaban) 

Ramadan or Ramasan , 

Schewwal (Schaouel, Sawal) 

Dsu '1-kade (Zaulkadeh, Dulhajee) 

Dsu-'l-hedsche (Zaulhedghe, 'lhijah) 



No. 



Dist. 



1 





2 


30 


3 


59 


4 


89 


5 


118 


6 


148 


'l 


177 


8 


:07 


o 


236 


10 


2C6 


11 


2C5 


12 


325 



And the 12th month has 29 days in a common year, but 30 days in a year marked 
K (Kebices) in ME. Rule 1. 

1 



ME. 

ME. Rule 3. For ME. into AD. Divide the year ME. by the circle 30 for Q of 
past cycles +R=GN. Then multiply Q by 10,631, and to P add the number 
which in Eule 1 is opposite to GIST., and the number which in Rule 2 is opposite to 
the name of the given month and the given day of the given month and the con- 
stant 227,015 and S=DAD.=Days AD. 

Then divide DAD. by 1461 for 1st Q and 1st R. Divide 1st R by 365 for 2d Q 
and 2d R. Then multiply 1st Q by 4 and to P, add 2d Q and the constant 1, and 
S=year AD. Then 2d R=day of Jan. OS., to which add NS. SC. for Jan. NS. 

ME. Rule 4. For AD. into ME. From Jan. NS. subtract NS. SC. for Jan. 
OS. Then subtract one from the year AD. and divide 1st R by 4 for Q and 2d R. 
Multiply Q by 1481 and 2d R by 385. To these products add the day of Jan. OS. 
and S=DAD. From DAD. subtract the constant 227,015. Divide R by 10,631 for 
Q and 2d R. From 2d R subtract the number which in Rule 1 is next less for 3d 
ll, and reserve the GN. opposite. Then from 3d R subtract the number which in 
Rule 2 is next less, and 4th R=day of the month opposite to the last number sub* 
tracted. Then multiply Q by 30 and to P add GN. and S=Year ME. 



ME. RuleS. For Ferial. Subtract one from DAD., and 
divide R by the circle 7 and 2d R, 1 to 7= Sunday to Sat- 
urday. 



ME. Rule 6. Special dates. 1st Muharrem=A'id-el-riachab=]Srew Year=a feast. 
The 10th Muharrem=Ashoura is a very rigorous fast. The 12th Rabi-el-aouel= 
Mevloud=day of birth and death of Mohammed. The 12th Djemasi-el-aouel is the 
anniversary of the capture of Constantinople. The 29th Redjeb= ascension of Mo- 
hammed on the ass Borak or Bulak. The 15th Chaban= anniversary of the total 
descent of the Koran. Ramadan for the whole month, fast during the day and 
banquets at night. The 27th Ramadan=Lailat-el-kadr=night of power=beginning 
of the descent of the Koran. 1st, 2d, 3d Chaoul=Bairam Kutchuck=feast of the 
Little Bairam= Ai'd-el-saghir= Aid-el-fatah, when they express great joy for the end 
of the fast, and make extraordinary prayers in the mosks. The 10th Zoulhedghe= 
Beiram Buy ouk = Grand Beiram = Ai'd-el-habir = Aid- el-corban = Aid- el-adhha = Mo 
hammedan passover, when victims are slain. 

Monday is for marriages. Wednesday is a holy day as Sunday with us, or as 
Saturday with the Jews. The 13th, 14th, 15th days of the month are fortunate. 

ME. Examples. 

ME. 1st Ex. Ideler (p. 466) gives ME. 387 Schewwal 29. Then 367-^-30=Q 12+ 
GN. 7=GND. 2128. Then 12xlO,631+GND. 2126+ Schewwal dist. 266+ day 29+ 
constant 227,015=DAD. 357,008 ;-i-1461=Q 244+R 524 ;-=-385=2d Q 1+Jan. 159 
OS.=June 8. Then Q 244x4+2d Q 1+constant 1=AD. 978. .June 8. 

ME. 2d Ex., with constant 227,015, dated OS. 

Standard ME. 1, M 1, D 1=AD. 622 July 15. 

Ideler (p. 466) ME. 367. .M 10. .D 29=AD. 978 June 8. 

Journal Asiatique (p. ) ME. 1228. .M 1. .D 1=AD. 1812 Dec. 22. 

2 



l=:Youm 


-el-ahad. 


2= " 


" thany. 


3= « 


" thaleth. 


4= " 


" arbaa. 


5= " 


" klanis. 


6= " 


" djoum. 


1= " 


" sabt. 



ME. 

Phil. Trans ME. 1228. .M 1. .D 1=AD. 1812 Dec. 22. 

«' ME. 1251.. Ml.. Dl= AD. 1835 April 16. 

ME. $d Ex., with constant 227,016, dated OS. 

Conn, des Temps ME. 1251. .M 1. .D 1=AD. 1835 April 17. 

Conn, des Temps ME. 1201 . .M 1. .D 1=AD. 1786 Oct. 13. 

Greenwich Naut. Al ME. 1273. M 1. .D 1=AD. 1856 Aug. 21. 

American Naut. Al ME. 1273. .M1..D 1=AD. 1856 Aug. 21. 

ME. 4th Ex. Rule 4, with constant 227,015 dated OS. Greaves' tables AD. 1783 
Nov. 14 OS. Jan. 318=M 1. .D 1. Then 1783-1 ;-^4=Q 445+R 2. Then 445X 
1461 +2X365+ Jan. 318=DAD. 651,193 -.-227,015 ;-=-10631=Q 39+R 9539. Sub- 
tract 9568 GND. of GN. 28, leaves Day 1 ; subtract the next less in table 2, leaves 
M1..D 1. Then Q 39X30 + GN. 28=Year ME. 1198. .M 1. .D 1. 

Also, AD. 1784 Nov. 2 OS.=ME. 1199 M1..D1. 

ME. 5th Ex. Rule 4 with constant 227,016, dated OS. This makes the dates of the 
1st Muharrem fall one day later than in the 4th Ex. , and this will agree with alma- 
nacs printed in Calcutta, according to the usage of the Mahometans of India. So 
says Marsden, Phil. Trans. AD. 1788, Vol. 78, p. 424. (4, 6, 7, 25.) 



ME. NOTES. 

ME.=MOHAMMEDAN ERA=TURKISH CALENDAR. 



(1). These rules count from Thursday, July 15, AD. 622, in civil time from 
sunset after noon, and one day less than the same actual date Friday, July 16, 
AD. 622, in Mohammedan time counted from sunset before noon. 

(2). This is an important difference, and when giving rules or dates, precision re- 
quires the statement whether it is civil time or Mohammedan time. Thus : MD. 
makes mean new moon at Mecca fall AD. 622, July 14. .1 h. .26 m., A.M. Ideler 
(p. 485), in a note, says that mean conjunction at Mecca fell AD. 622, July 14. .1 
h. .12 m., A.M., thus differing only 14 minutes from MD. But he says that ac- 
cording to Delambre's tables, the true date of conjunction at Mecca was July 14. . 
8 h. .17 m., A.M., and on the 15th July the moon became visible before evening. 
This is high authority, since Ideler was the Astronomer Royal at Berlin. Then 
(p. 459), he says : ' ' Niebuhr says ' the day on which the new moon first appears is 
the first day of the month. When the heavens at the time of new moon are cov- 
ered with clouds, the month begins a day earlier or later. '. '. . . The astronomers of the 
Sultan at Constantinople make each year a new almanac, which they constantly 
carry with them. By the Arabians I have seen nothing like this." 

(3). Marsden says : " The Arabians and Syrian-Christians and Mahometan astrono- 
mers generally appear to have fixed the day to Thursday," but in later times it has 
been fixed to Friday. The moon became visible at Mecca on the evening of Thurs- 
day, "which was to them the commencement of Friday (beginning a few hours 
later), which we term the 15th July." Pierce (Vol. 8, p. 153) says that the Hedschra 
was "on the 15th (not 16th) July, AD. 622." But (p. 721) he says that in making 
this reduction, the difference between the time at which the day begins in the Turk- 
ish and Christian calendars must be taken into consideration .... as it may make a 
difference of one day more or less. Francos ur (p. Ill) says that the Mahometans 
determine the date by observation. The rule gives the mean date for the learned, 
and at times varies two or three days. But they generally give the day of the week, 
and that removes all doubt. " According to M. Ideler, conjunction fell 14 July, 
6 h. .22 m., mean time [? 2]. Therefore the crescent was visible 15th July in the 
evening, and the month Muharrem fixed by this appearance must commence 16 
July." 

(4). This last remark shows that ME. 3d Ex., from Con. des Temps, must be 
understood to be in Mohammedan time on the basis of July 16, as also the examples 
ME. 3d Ex. from the English and American Nautical Almanacs, which only give the 
dates, and ME. 5th Ex. from the Almanac in Calcutta, and the Oxford Chrono- 
logical Tables, which give the date of the Hegira, July 16, 622. Also Weber says 
that Mohammed was compelled to fly from Mecca to Modina 16th July, 622. " The 
Mohammedans reckon their years from this event, which is called the Hegira." 
But the rules give one day less than these Mohammedan dates, because in civil 
time on the basis of July 15, in accordance with the rule given by Ideler and ME. 

4 



ME. NOTES. 



ME. 


AD. by Rule 3. 


Marsd. 


1 


622 July 15 


July 16 


1228 


1812 Dec. 22 


Dec. 22 


1251 


1835 April 16 


April 16 


1201 


1786 Oct. 12 


Oct. 13 


1273 


1856 Aug. 20 


Aug. 19 


1198 


1783 Nov. 14 


Nov. 15 


1199 


1784 Nov. 2 


Nov. 3 



1st Ex. from Ideler, and ME. 2d Ex. from Ideler, and the Journal Asiatique and 
the Phil. Trans., and ME. 4th Ex. by Greaves. 

(5). Contra. Clemens Petersen, in Johnson's Cyclopedia (Mohammed) says : " The 
famous Hedjrah or flight from Mecca to Modina (250 miles) occurred Sept. 20, 
622, from which date the Mohammedan era begins." 

(6). Contra 2d. Marsden (p. 424) says : "Note. — According to the original table by 
Greaves the first day of Moharram in 1783 falls 14 Nov., OS., or 25 Nov., NS., 
and in 1784 on 2d Nov., OS., or 13 Nov., NS., whereas by two almanacs printed 
at Calcutta in Bengal, it appears that the days should be the 26th and 14th Nov. . . . 
both founded on the usage of the Mahometans of India," This shows that Mars- 
den thinks Greaves in error, and that he does not recognize the difference of a day 
as arising from a different mode of counting time, as shown in the examples, 
where the 2d and 4th use the same constant 227,015, and the dates by these al- 
manacs require the constant 227,016. 

(7). Contra M. The adjoining comparison 
of ME. Examples has first the year ME., then 
the date OS. in AD. for ME. 1, M. 1, D. 1, 
in civil time on the basis of the beginning of 
ME. in AD. 622, July 15, at sunset, by ME. 
Rule 3. Then the date OS. of the same 
years ME., from Marsden's table of dates 
from AD. 622 to AD. 2000, copied into 
Rees (Hegira) with the remark that "Mr. 
Marsden .... has given a very valuable table 
.... in which he has improved upon those in Greaves," etc. But these few dates, 
which accidentally occurred in ME. examples, show that his dates are not reliable, 
because not uniform. He counts in Mohammedan time on the basis of July 16 in 
ME. 1, 1201, 1198, 1199, like the three nautical almanacs in ME. 3d Ex., and like 
the almanacs in Calcutta in the 5th Example. Then in civil time on the basis of 
July 15 in ME. 1288, 1251, like ME. Rule 3, and Ideler, and Journal Asiatique, in 
ME. 2d Ex., and even like Greaves (whom he condemns as to these same dates) in 
ME. 4th Ex. Then in ME. 1273, on the basis of July 14, like no one else. The 
reader has the rules before him, and can criticise this criticism. 

(8). ME. Rule 1. To construct the Cycle. Ideler quotes the rule from the Arabic of 
Abu 'lhassan Kuschjar, and says substantially, that 12 months alternately 30 and 
29 days=354 days. But 12 mean lunations are counted 8 h. .48 min. in excess. 
Add this excess per year and when the hours exceed 12, make the last month 80 
days. This makes the embolismic years=2, 5, 7, 10, 13, 16, 18, 21, 24, 26, 29, as 
in the table. Then : 

(9). Begin with zero, at GN. 1, and for the distance of the beginning of GN. 2 after 
the beginning of the cycle add 354 days for a common year. Then to GND. of 
the embolismic year GN. 2 add 355 days. And thus continue to add 354 days to 
the GND. of a common year and 355 days to the GND. of an embolismic year, 
making 10,631 days in the cycle of 360 months in 30 years. 

(10). If the months were uniformly 30 and 29 days, the cycle would contain 10,620 
days. But the 11 embolismic days additional make it 10,631 days. And 360 mean 
lunations of 29.530,589 days =10, 631. 012, 040 days. So that this calendar makes 
the Turkish crescent grow less at the rate of one day in 2491 years. . 

5 



ME. NOTES. 

(11). Contra 1st. Ideler puts 354 opposite to year 1, and all the other numbers one 
year earlier than in ME. Rule 1. But the embolismic years and the numbers are 
the same. This arrangement is used as an improvement upon Ideler's arrangement. 

(12). Contra 2d. Francceur, and the Journal Asiatique, use Ideler's table, except 
that in place of making GN. 16 the embolismic year, they substitute GIST. 15. This 
is astronomically more accurate than Ideler's table. This was doubtless known by 
Ideler, since by the Arabic authority which he quotes, he states the excess at 8 h. . 
48 m., which makes GN. 16 the embolismic year, while at the same time (p. 479) he 
gives the actual excess 8 h. . .48 m. . .36 s. =0.367,083, and this in GIST. 15 makes the 
excess 5.506, and this being more than 12 hours would astronomically make GIST. 15 
the embolismic year. The present object is to find dates as the Mohammedans find 
them, and not to show how their calendar can be made more accurate by the small 
fraction of a day. (Conn, des Temps of 1844, agrees with Ideler.) 

(13). Contra 3d. Scaliger (p. 139) gives a table with the embolismic years 2, 5, 8, 
10, 13, 18, 19, 21, 24, 27, 30. Here he differs in the years 8, 19, 27, 30. 

(14). MB. Rule 2. To construct the Table. Begin with zero at Month 1, and add 
alternately 30 and 29 days, making the last month 29 days except in the embolismic 
years marked K (Kebices) in ME. Rule 1, change the last month from 29 to 30 
days. This makes the number of days opposite to tha name of the month, the dis- 
tance from the beginning of the year to the beginning of the month. 

(15). Contra. Ideler, and those who copy his rules, give the same number of days 
one month earlier. This arrangement is used as an improvement upon the arrange- 
ment of Ideler, when finding dates by ME. Rule 3. 

(16). Ideler gives the first series of the names of the months. Those in parentheses 
have been found elsewhere. In a note, he says : ' ' These names are written as 
near as may be to the Arabian language. The Persians and Turks say Dschemasi- 
ulewwel, Dschemasiulachir, Ramasan, Ssilhade, Ssilhidsche." And since Ideler 
writes in German, his names must be pronounced accordingly. 

(17). ME. Rule 3. For date AD. As defined in the beginning, these rules count from 
July 15 AD. 622 in civil time. Then the constant DAD. (Days AD.) 227,015 is 
one day less than the date AD. 622 July 15, and therefore the distance from AD. 1 
Jan. 1, to the beginning of ME. Then Qxl0,631 is the distance from the begin- 
ning of ME., to the beginning of the current cycle. Then GND. opposite to GN. 
is the distance from the beginning of the current cycle to the beginning of the cur- 
rent year. Then the distance opposite to the name of the month is the distance 
from the beginning of the year to the beginning of the given month. These are all 
cardinal numbers, because actual distances from point to point, and at each point 
require the addition of one day to convert distance into date, because all measures 
of time (except modern hours and its parts) are ordinals and begin with One, not 
zero. This ordinal one is added to convert the sum of the distances into the date 
required by adding the day of the month which begins with one. And NS. SC. =12 
days from March 1, 1800, to March 1, 1900, then 13 days to March 1, 2100. Also 
10 days from Oct. 5-15, 1582, to March 1, 1700, then 11 days to March 1, 1800. 
The rules are given in OS., because in OS., every year, including the centurial 
years AD., which leaves no remainder when divided by 4, is a leap year (JC. 0). 

(18). Contra. All others as far as known, use the rule given by Ideler (p. 466), 
thus condensed by the use of symbols, viz.: Divide the ''past year" ME. by the 
circle 30, for Q and R. Multiply Q by 10,631. Add the sum in table 2 [ME. 
Rule 1, with GND. one year earlier] "and the day sum of the past month in 

6 



ME. NOTES. 

table," [ME. Rule 2, with distances one month earlier] and the day of the month 
and 227,015. Then divide this sum by 1461 for Q and R. Multiply Q by 4 and 
add as many times as 365 will go into R, and to these add one for the year, and 
2d R=day of Jan.— Example. 29 Schewwal 367. Then the past year 366-^30= 
Q 12+R 6. Then 12x10,631=127,572+2126 for R 6+226 for 9th Month+29 day 
of Schewwal +227, 015 =357, 008 sum ;-=-1461 = Q 244+R 524 ; 244x4=976+1 for 
524 -i- 365, +1= AD. 978, and R=Jan. 159= June 8 (ME. 1st Ex.). 

(19). Now. Those who prefer Ideler's rule can make the changes enclosed in 
brackets. But ME. Rules 1, 2, 3 are considered improvements. There are unneces- 
sary complications in Ideler's rules which may cause errors in the calculations. He 
does not divide the given year, but the "past year" to find Q and R. This subtrac- 
tion -of a year is unnecessary. And it makes his artificial cycle begin one year before 
ME. began. And it finds R, one year before the year GN. of the cycle, so that it 
makes the first year of the current cycle, the last year of the previous cycle. And 
since he does not advance his marks for the embolismic years along with his 
distances, he will put the embolismic day in the wrong year, unless he takes one 
year later than he finds by rule. Then he does not take the distance opposite to 
the name of the given month, but "the day sum of the past month," and in his 
example uses the number opposite to Ramadan to find the date in Schewwal. And 
to find the date in Moharrem he must use the number opposite to Dsu-1-hedshe, 
which will be 354 if the year be a common year or 355 if an embolismic year, with 
the complications arising from dividing " the past year" by 30. 

(20). On the contrary, ME. Rule 3 divides the given year by 30, and thus makes 
the first cycle begin with ME., and gives R the actual GN. of the current cycle. 
And GN. shows whether the year is embolismic, requiring the last day to be embolis- 
mic. And the distances are opposite to the names of the months. And there is 
no complication in an embolismic year, since the only difference is in counting the 
last month 30 days when the date happens to fall on that day. 

(21). ME. Rule 4. For AD. into ME. This is the reverse of ME. Rule 3. Nothing 
analogous has been met with, but may exist. One year is necessarily subtracted 
from the year AD., to throw the effect of the intercalary in a leap year upon all 
the dates of the next year. 

(22). ME. Rule 5. For the Ferial. This is the shortest mode in the present case, 
because DAD. has been found to find the date. And AD. 1, Jan. 1 was Saturday. 

(23). ME. Rule 6 requires no explanation. 

(24). ME. Examples 1st, 2d, 4th, show the civil date upon which the ME. day 
begins at sunset, while 3d and 5th show the Mohammedan date one day later by 
counting the day as beginning on the previous evening, analogous to the Hebrew 
mode of counting time. 

(25). The Authors referred to above areldeler, Lehrbuch der Chronologie, Berlin, 
1831, pp. 455-476. And Marsden in the Philosophical Transactions, London, AD. 
1788, Vol. 78, pp. 414-432. And Francoeur in the Connaissance des Temps, or 
French Nautical Almanac, Paris, 1844, p. 111. And Journal Asiatique, Paris, 
1827, 1st Series, Vol. 2. And Scaliger, De Emendatibne Temporum, Geneva, 
1629, pp. 135-148. And Rees' Cyclopedia (Hegira). And Nautical Almanacs, 
English (GNA.), French (PNA.), American (ANA.), which give annually the be- 
ginning of the year ME. as in ME. 3d Ex. And Pierce's Universal Lexicon and 
Oxford Chronological Tables, and Johnson's Cyclopedia (Mohammed), and Weber's 
Outlines of Universal History. 

7 



1. KfC. = Nicean Calendar, or " Alexandrian Canon," was introduced in the cen, 
.my after the Council of Nicea, in AD. 825, to represent the following 

2. Nicean Rule. The Council gave no astronomic rule, but in general terms de- 
creed that Easter should be held on Sunday on or after the first day of the Passover, 
and not on the 14th day of Nisan as practised among the Asiatics, who were thence 
called " Quartodecimans," or Fourteenth day men. This being an astronomic date, 
and the Egyptians being most skilled in astronomy, the Council commissioned 
the Bishop of Alexandria to procure this date in advance, in place of the Jewish 
mode of waiting for the appearance of the new moon, as practised during the 
Second Temple (NB. AO. 11). " Ne cum Judceis conveniamus" (Missal.) 

3. This NC. consisted of two parts. The lunar portion was the cycle of 235 new 
moons in 19 years (= NC. NGN. in NB. GND.), and the solar portion determined 
" March 21 " to be accounted the Vernal equinox, by what are called the Paschal 
Canons, viz. : 

" 1st. That the 21st day of March shall be accounted the Vernal Equinox. 2d. 
That the full moon happening upon or next after the 21st day of March, shall be taken 
for the full moon of Nisan. 3d. That the Lord's day next following shall be Easter 
day. 4th. But if full moon happen upon a Sunday, Easter shall be the Sunday 
after " (Wheatly, p. 86). This is given in substance in the Anglican Prayer Books. 

4. This calendar was probably the work of the Egyptian astronomers, who had 
previously predicted the date of Easter as the result of astronomical calculations. 
The rule (MDB.or MDK. ; or MDT. in (NB. AC. 2, 16) shows that new moon fell on 
March 31, AD. 325 ; and NC. NGN. compared with AIL NGN. in (NB. GND.) shows 
that the Roman Calendar of BC. 45 was modified by changing the Basic year from 
BC. 45 to BC. 1 ; or the first year in which AU. recovered from its confusion (NB. 
AU), and at the same time that one day was subtracted for the lunar recession ; 
thus agreeing with the actual recession of one day in 308 years when counted in 
Julian years. Also, March 21 was the artificial maximum Julian Civil date at Jeru- 
salem of the Vernal Equinox in AD. 325 and thereabouts, while its Calendar or 
actual date in AD. 324, 325, 326, and in each four years before and after these dates 
it was March 20, and only in AD. 327 and in each third year after leap year about 
that date was it as late as March 21. (NB. Calendars 18—4). Hence, while retain- 
ing the scale of the Roman Cycle, which admits of only a single date as the limit 
(NB. Scale), they adopted the latest date of the Vernal Equinox, and thus prevented 
Easter from falling contrary to the Nicean rule on the day of full moon, as it 
would have done in each third year after Leap year, when full moon fell on March 
21 and on Sunday, had March 20, the actual date in AD. 325, been given as the 
single date of VGND. 

5. But NC. NGN. gave only the date of new moon, and to this date, some added 
12, others 13, and others 14 days for the full moon of Nisan, until in AD. 527 by 
common consent the Alexandrian Canon was adopted, and 13 days were added to 
make the 14th Nisan; on which day Christ was crucified; and this was confirmed 
by the Council of Chalcedon in AD. 534 in the form of OS. FGN. (OS. 2), and of AM. 
FGN. (AM. 4), as shown in (NB. GND. 12, 13). (Wheatly, p. 38.) 

6. The following historical statements indicate the above : " The Fathers did 
not give this Canon. The rules are in a letter to the Church of Alexandria. The 
letter does not exist, but we know the spirit of it." And " the paschal moon was 
that of which the 14th day coincided with the Vernal equinox or next after" 
(Delambre, Vol. I., p. 3). '"This determination of the equinox is not among the 

* See NS. Preface. 1 



JVC. 

Canons of the Council, but may be seen in the Synodic Epistle preserved to us by 
the two ecclesiastical historians, Socrates and Theodoret;" and " The 14th Nisan 
being the Jews' Passover " (Long, 1255). " No such Canons are found in the proceed- 
ings of the Council," and " The Patriarch of Alexandria was commissioned to 
announce the time of Easter" (Neale, p. 113; Seabury, p. 76). "The Fathers of the 
century after the Council of Nicea ordered the new and. full moons to be found by 
the cycle of the moons consisting of 19 years " ( Wheatly, pp. 36, 37). Most of the 
Churches used the ancient Jewish cycle of 84 years" (Brady, p. 295, and Seabury, 
p. 78, quoting Prideaux). '* Passover on 14th of the Paschal month" and " 14th 
Nisan" (Seabury, pp. 70, 73). " The full moon of Nisan was the 14th of the moon's 
appearance" and " The Roman Church changed its cycle in 455, 457, 525, 1582" (Brady, 
p. 294). " The 14th of the Calendar month" (Greek " Book of the Litany "). " In 
AD. 455 S. Pretorius gave Easter correctly April 24, but the Western Church held 
it April 17" (Neale, p. 113). " No effectual cure was found till Dionysius Exiguus, 
AD. 525, brought the Alexandrian Canon entire into the Roman Church, and this 
was adopted with entire unanimity" (Seabury, p. 78, quoting Prideaux). Wheatly 
(p. 38) gives this cycle of Dionysius = OS. FGN. (NB. GND.) as confirmed by the 
Council of Chalcedon, AD. 534. " In AD. 527 the Romans abandoned Nisan 16 as 
the earliest date of Easter, and following Dionysius, adopted Nisan 15, as had pre- 
viously been used by the Bishops of Alexandria, while the British and old Irish or 
Scotch had previously used Nisan 14" (Seabury, pp. 87, 88, 89). The decision was 
first made by the Council of Aries, AD. 314, and confirmed by the Council of 
Nicea, AD. 325. (Brady, p 295.) (Neale, p. 147.) 

CONTRADICTIONS. 

(1.) Jarvis (pp. 94, 95) says that the Vernal Equinox had receded from March 
25 to March 21 by the " Precession of the Equinoxes " in place of the error of the 
Julian Calendar. (AC. Notes 94-101.) 

(2.) Also, Jarvis (pp. 87-92) gives the full cycle NC. NGN. (NB. GND.) as " estab 
blished by the Council of Nice. " 

(3.) All the following assert or imply that the actual date of the Vernal Equinox 
in AD. 325 was March 21, viz : Long (1255) ; Montucla (Vol. I., p. 582) ; Renwick 
(Vol. II., p. 201); Rees (Calendar); Adams (Roman Tear); Missal (De Festibus Mo- 
bilibus); Jarvis (pp 95, 96); Wheatly (pp. 35-38); Seabury (pp. 105, 110, 118). 
But Seabury (p. 190) quotes the British Act of Parliament of 1751, as "on or 
about the 21st day of March." (AC. Notes 12-16.) 

(4.) Wheatly (p. 37) says: " For want of better skill in astronomy, the Paschal 
Canons confined the equinox to March 21." 

(5.) Rees (Canon Paschal) and the Encyclopedia Britannica says that NC. is 
attributed to Eusebius of Caesarea, and to have been constructed by order of the 
Council of Nicea. (AC. Notes 1-11, 17-26, 81-131.) 

2 



NE. 

NE.=ERA OF NABONASSAR. 



This ancient Egyptian calendar was taken to Babylon, and counts from JP. 3967 
February 26. 

NE. Rule 1. For NE. into JP. Multiply the year NE. by 365, and to P add 
the day of Thoth (Rule 3d), and the constant 1,448,272 and S=DJP., which re- 
duce (A). 

NE. Rule 2. For JP. into NE. From DJP., subtract 1,448,272. Divide R by 
365 for Q=year NE., and 2d R=day of Thoth, which reduce by Rule 4. 

NE. Rule 3. For the day of Thoth, add the given day of the given month, to 
the number prefixed to that month, in the following table : 0+ Thoth ; 30+Paopi ; 
60-^-Athyr; 90+Choiak ; 120 + Tybi; 150+Mecheir ; 180 + Phamenoth ; 210+ 
Pharmouthi ; 240 + Pachon ; 270 + Payni ; 300 + Epiphi ; 330 + Mesori ; 360 + 
Epagomenai, of which there were 5=365 days in a year NE. 

NE. Rule 4. For the day of the month. From the day of Thoth, subtract the 
numbers in the table in Rule 3, which is next less than the day of Thoth, and R= 
day of the month, to which that number is prefixed. 

NE. 1st Ex. Lunar eclipse at Babylon NE. 27, Thoth 29 at 9 hours 30 minutes 
after noon : Then 27x365+29+l,448,272=DJP. 1,458,156. Then DJP. 1,458, 
156-365 ;-5-1461=Q 997+R 1174 ;-=-365=2d Q 3+ Jan. 79. Then 997x4+2d Q 3+ 
constant 2=JP. 3993. Then 3993-1 ;-^-4 leaves JC. (bissextile) and Jan. 79= 
March 19 at 9 h. .30 m. after noon. 

NE. 2d Ex. Summer solstice at Athens NE. 316, Phamenoth 21, at 5 or 6 hours 
after midnight. Then Phamenoth 21 +180= Thoth 201. And NE. 316 Thoth 201 
=DJP. 1,563,813=JP. 4282 June 27, at 5 or 6 hours after midnight. 

NE. Sd Ex. Scaliger (pp. 198-9). JP. 4713 Aug. 23. Then JP. 4713-1 ;-r-4 
leaves JC. 0, and Aug. 23= Jan. 236. Then .4713-2 ;h-4=Q 1177+R 3 ; 1177X 
1461+3x365+constant 365+ Jan. 236=DJP. 1,721,293. Then 1,721, 293 -constant 
1,448,272 ;--365=Q 748=year NE.+R l=Thoth 1st. 

NE. Uh Ex. Lunar eclipse at Alexandria NE. 366 Thoth 27 at 6 h. .30 m. after 
midnight (Jarvis, p. 119). Then NE. 366 Thoth 27=DJP. 1,581,889=JP. 4331 
Dec. 23 at 6 hours 30 min. after midnight. 

NE. 5th Ex. Lunar eclipse at Alexandria NE. 547 Mesori 16th, at 7 hours after 
noon (Jarvis, p. 120). Then Mesori 16 +330= Thoth 346. And NE. 547 Thoth 
346=DJP. 1,648,273=JP. 4513 Sept. 22 at 7 hours p.m. 

NE. 6th Ex. Censorinus (Jarvis, p. 120) says that in NE. 986, Thoth 1st fell on 
June 25. Then 986x365+l+l,448,272=DJP. 1,808,163=JP. 4951 June 25. 

NE. 7th Ex. AE. began JP. 4685 Aug. 30 (in JC. 0)=Jan. 243=DJP. 1,711,073 ; 
-1 448,272=262,801 ;-*-365=Q 720=NE. 720+R l=Thoth 1st. But the Romans 
called this August 29. (JE., AE.) 

1 



NE. NOTES. 

NE.=ERA OF NABONASSAR= ANCIENT EGYPTIAN CALENDAR. 



(1). As to Rules 1 and 2. NE. began JP. 3967 Jan. 57=DJP. 1,448,638. Then 
to leave room for NE. lx365+Thoth 1, subtract 366 and leave the constant 1,448,- 
272. 

(2). The examples compared with astronomic dates by MD. in the Appendix, 
prove that both rules are correct — observing that MD. gives the mean date, from 
which the date of actual full moon varied 0.568 more and less than the mean, in the 
standard cycle of variations, from 1853 Sept. 17. .10 h. .12 m., to 1854 March 14. . 
17 h . . 53 minutes standard time. 

'3). As to 1st Ex. This is the earliest definite date of an eclipse, 2600 years before 
AD. 1880, and 114 years before the Jewish Captivity. It is quoted by Tycho 
Brahe (Prol. , p. 3) from Ptolemy of Alexandria (Aim. Lib. 4, Chap. 6). The date 
here found is JP. 3993 March 19.895,833 counted from midnight, while MD. 2d 
Ex. makes mean full moon fall JP. 3993 March 19.467,827 counted from midnight 
at Babylon. Hence the actual was 0.428 more than the mean. (2, 17, 19-35.) 

(4). As to 2d Ex. This is the earliest solar date on record, 2300 years before AD. 
1869, as determined by Meton and Euctemon as the basis of the Olympic Era (OE.). 
It is given by Tycho Brahe (Prol., p. 6). They made the date 5 or 6 hours after 
midnight, while MD. 4th Ex. makes the date at Athens 8 hours 5 minutes after 
midnight. The difference of 2 hours is probably as near as they were able to de- 
termine the time when the sun was furthest north ; by the shadow of an obelisk 
and without the assistance of modern time-keepers. (17.) 

(5). As to 3d Ex. This is given to compare with Scaliger's mode of reduc- 
tion. (10.) 

(6). As to UK Ex. This eclipse fell JP. 4331 Dec. 23.270,833 counted from mid- 
night. MD. makes mean full moon fall JP. 4331 Dec. 23.597,137 counted from 
midnight at Alexandria, so that the actual was 0.326,304 less than the mean. Jar- 
vis (p. 119) says that this is in Ptolemy's fourth book, and uses this example to 
show his mode of reduction, and to prove that NE. began JP. 3967 Feb. 26. (2, 12.) 

(7). As to 5th Ex. The eclipse fell JP. 4513 Sept. 22.791,667, while MD. makes 
mean full moon fall JP. 4513 Sept. 22.361,209 at Alexandria. Hence the actual 
was 0.430,458 more than the mean (2). Jarvis (p. 120) says that Petavius calculates 
this eclipse at Sept. 22 7 h. .15 m. p.m. = Sept. 22.802,083. 

(§). As to 6th Ex. This verifies NE. Rule 1. 

(9). As to 7th Ex. This proves that the imperial edict made no change in the 

2 



HE. HOTES. 

first year of the Actian Era, "but required that thereafter Thoth 1st must always 
fall on the same Koman date as it did in the first year. (AE.) 

(10). These NE. rules are original and more simple than the rules given by Sea 
liger (pp. 198-206), and by Jarvis (pp. 118-120). The 3d Example is thus reduced 

by Scaliger : " Example. The common year of Christ is JP. 4713. Subtract 

3967 from 4713 leaves 747 Julian years, from the end of December 3967 to the end 
of December 4713 ; but under the ratio of NE. from Feb, 26. .3967 to Feb. 26. . 
4713. Therefore subtract 56 days and there remain 746 solid Julian years and 309 
days. The Julian Bissextiles for 746 years, that is 186 days compounded with 309 
days make 495, that is one Egyptian year and 130 days. Therefore from the 1st 
Thoth NE. to the end of JP. 4713 are 747 absolute Egyptian years and 130 days, 
besides the days of NE. 748 unfinished. Subtract 130 from 365 and there remain 
235 days from the Kalends of January, terminating in August 23 inclusive. There- 
fore Thoth 1st fell at that date." (5.) 

(11). This requires more figuring than the present rule, with the greater objec 
tion, that the principles must be constantly kept in mind and properly applied to 
prevent false results. While the present rules, like all the other rules herein, are 
prepared to be worked by rote, so that the whole attention may be devoted to the 
accuracy of the figuring. 

(12). Jarvis (p. 119) reduces the 4th Example thus : " The first step to be taken 
is to turn the Egyptian into Julian or Roman years ; and this is done by multiply- 
ing them by 365 to turn them into days, then dividing them by 1461 the number 
of days in four Roman years, and multiplying the quotient by 4. The remainder 
will be the number of days in the next Roman year. As Thoth is the first month 
in the 366th Egyptian year, and the eclipse took place 6 h. .30 m. after midnight 
on the 27th of that month, the sum must be stated thus : 

365 y. 26 d. 6 h. 30 m. 1461) 133,251 ( 91 
365 4 



Rem. 300 |364 

Days 133,251, 6 h. 30 m.=R. y. 364, 300 d. 6 h. 30 m. From the 1st of January 
to the 22d December inclusive in the year 4331 of the Julian Period were 356 days. 

Therefore from A. J. P. 4330. .356 d. 6 h. 30 m. 
Subtract 364 300 6 30 



And there remain 3966 56 

Fifty-six days are equal to Jan. 31 to Feb. 25. Consequently, the iEra of Nabo- 
nassar began on the 26th of February, in the year 3967 of the Julian Period." 

(13). Newton (Vol. 5, p. 284) says that the Egyptian mode of counting time— 
which he calls "Thoth"— was taken to Babylon in JP. 3967, when Thoth fell 
33 days 5 hours before the vernal equinox. The above examples prove that NE. 
counts from JP. 3967 Feb 26. Rees (Epocha) says that NE. began Feb. 26 at 
noon. But Long (Sec. 1211) quotes Censorinus, who says, that the Egyptians and 
ancient Romans counted from midnight. 

(14). Jackson (Vol.2, p. 8) says that Thoth=Sothis=Isis=Egyptian Venus= 
Sirius^Dog Star. That Geminus of Rhodes, says that in his time (BC. 77) the 
heliacal rising of Sirius was 30 days after the Summer Solstice. And (p. 9) that 

3 



NE. NOTES. 

Pliny says, that the Dog Star rose when the sun entered Leo, 15 days before the 
Kalends of August (July 18). 

(15). This heliaeal rising of the Dog Star was at that time a very important 
date in Egypt, since at that time the Nile began its annual rise. The near approach 
of this time was indicated by the heliacal rising of a Canis Minoris, which was 
called Procyon, from the Greek Prokuon=before the dog. And Dog-days derived 
their name from the rising of the Dog Star. But the precession of the equinoxes 
now causes Sirius to rise about a month later in equinoxial time, so that it no 
longer has the same importance as about 2000 years ago. (28.) 

(16). This year was called the " Wandering Year," because it uniformly con- 
tained 365 days, and therefore receded a full Julian year in 1460 Julian years. It 
was also called the Canicular year, from Canicula the Dog Star. And the great 
Egyptian period was counted from the " Year of God" (i. e., of Sothis) when Thoth 
1st coincided with the heliacal rising of Canicula, to the same sidereal period. And 
calculation makes this period about 1508 mean years in consequence of the preces- 
sion of the equinoxes. (26.) 

(17). This mode of recording astronomical phenomena is the best that has ever 
been used. And Scaliger (p. 431) says that " these years of the Chaldeans were 
not political and never were so, but mathematical." And Jarvis (pp. 118, 119) says 
that Ptolemy of Alexandria has " transmitted to us the oldest astronomical calcu- 
lations known, which under the direction of Aristotle (BC. 300 dr.), had been 
transmitted by Cailisthenes from Babylon to Greece, and afterwards adjusted by 
Hipparchus of Alexandria to the Egyptian mode of computing time." (3, 4, 21.) 

(1§). But, although NE. carries the name of Nabonassar, while it was only used 
by the astronomers of Babylon, it was evidently the popular calendar of the Egyp- 
tians, since the Actian Era of the Egyptians was the same as NE. with 12 consecu- 
tive months of 30 days and 5 epagomenai, except that an extra epagomenas was 
added by order of Augustus in the same year as the Roman bissextile, so that Thoth 
1st should always fall on the Roman August 29. (9 ; AE. Notes ; HC. Notes 115, 
124 ; 139-156.) 
(19). The New York Observer of Nov. 26, 1885, has the following : 
"Professor Sayce, in the Academy, writes of the Phainomena or Heavenly Dis- 
play of Aratos Of the original work, he says that it is not only ' curious 

and interesting of itself, but also valuable for the history of astronomy.' It is, in 
fact, a versification of the astronomical lore of Eudoxos, and though the astronom- 
ical knowledge of Eudoxos was probably but slight, while that of the poet was still 
less, it embodies the traditional information of the Greeks about astronomical mat- 
ters which we now know to have been derived by them from the East. It conse- 
quently formed the starting-point of later scientific Greek astronomy. Mr. Brown 
not only believes that the poem embodies the ideas ultimately derived from Baby- 
Ionia, but that the configuration of the stars as described by Aratos is itself of Bab- 
ylonian origin, and belongs to the second millennium before the Christian era. It 
is certainly inconsistent with the positions of the constellations in the time of Eu- 
doxos or Aratos, while a map attached by Mr. Brown to his third appendix shows 
how closely it agrees with the positions of the principal stars near the equator at 
the time of the equinox 2084 BC. In the Phainomena of Aratos, consequently, we 
have to see not a Greek chart of the heavens as they appeared in the fifth or third 
century BC, but a traditional representation of the stellar sky, as mapped out by 
Babylonians two thousand years before." (3, 24-26.) 

4 



NE. NOTES. 

(20). "The decipherment of the cuneiform inscriptions has pi oved two things, 
both of them, indeed, already divined by scholars, but from the nature of the case 
previously unverifiable. One of these is the fact that the signs of the zodiac were 
of Babylonian invention, the other that the configuration of the celestial globe took 
the shape in which it was received by the Greeks between BC. 2500 and 2000. The 
precession of the equinoxes prevents our placing it earlier than about BC. 2500. 
since before that date the sun at the vernal equinox would have entered Taurus, 
and not the first point of Aries, while the zodiacal cycle, as we find it in Bab- 
ylonian and Greek astronomy, begins with Aries. Accordingly, in my memoir 
on Babylonian astronomy, published eleven years ago, I concluded that the inven- 
tion of the Babylonian calendar, and the beginning of systematized Babylonian as- 
tronomy, must be assigned to about BC. 2000, though I admitted that the nu- 
merous records of eclipses incorporated in this systematized astronomy implied an 
enormous antiquity for the star-gazing Chaldeans." (22-35.) 

(21). "Mr. Furlong adds : 'I believe we may get near to its true date through 
Porphyry. He wrote that Callisthenes brought the Babylonian standard work on 
astronomy to Greece 2000 years before the time of Alexander the Great, so that the 
configuration of the stars and zodiacal figures, which Eudoxos and afterward Ara- 
tos and Hipparchus manipulated, would be at least as old as 2850 BC. I regret I 
have no books near me wherewith to follow up this subject.' The Chinese date 
their astronomical cycle and zodiac from 2640 BC." (3, 17, 37, 38.) 

(22), In the same direction, Smyth's Celestial Cycle (Yol. 2, p. 314) says of Thu- 
ban (a Draconis) : " Upwards of 4600 years ago it was the pole star of the Chal- 
deans, being then within 10' of the polar point ; a point which will not be ap- 
proached by a Ursa Minoris [the present pole star] nearer than 26' . . 30". a Dra- 
conis in that remote age must have seemed stationary during the apparent revolu- 
tion of the celestial sphere about the northern extremity of the polar axis ; though 
now it has by the slow movement to which the stellar host is subjected deviated 
from the pole as much as 24° . . 52'." 

(23). Now : The earliest definite astronomic date on record is given in NE. Ex- 
ample 1st at BC. 721. This is a historic fact. But the position of the stars at any 
date can be determined by calculation. The Admiral fixes the date BC. 2700, 
when the polar point was within 10* of Thuban. And he speaks as if the Chal- 
deans were witnesses of that fact. But this is in his usual playful mode of describ- 
ing astronomic facts. And he may not have thought of its bearing on history, 
since Ussier fixes the date of the Flood at BC. 2349. (3.) 

(24). On the contrary, the Professor's remarks refer to history, and he brings in 
evidence the writings of Aratos, Eudoxos, and Porphyry to prove that the Baby- 
lonian zodiac was framed about BC. 2500 or 2350. Now, Lempriere's Classical 
Dictionary says that Aratos wrote about BC. 277, and Eudoxos died BC. 352, and 
Porphyry died AD. 304. So that the earliest of these witnesses lived about 2000 
years after these dates, and probably did not know what changes had been made 
before their time. Even the Jews do not know when the beginning of their year 
was changed from Nisan to Tisri. But they do know that the change has been 
made within the last 2000 years. (HC. Notes.) 

(25). These writers are good witnesses to prove that in their day the zodiac began 
with Aries, and that tradition made the zodiac begin with Aries as far back as was 
known. And the Professor shows that Aries could not have been the first sign oS 

5 



NE. NOTES. 

the zodiac before BC. 2500. But he does not state that for the same reason calcu- 
lation cannot define the date when Aries was established as the first sign of the 
zodiac at. any year between BC. 2500 and about BC. 250. Thus : 

(26). Hamal (a Arietis) is the brightest star in the constellation Aries, and near 
its western border, so that if not the ancient " first point of Aries," it must be very 
near it. In 1886, the Right Ascension of Hamal is 2 hours and minutes. .44.86 
sec, or about 30 degrees, or one sign of the zodiac, East of the modern First point 
of Aries, which is the point where the sun crosses the Equator in the spring. The 
precession of the equinoxes at the present rate of 50.2601 seconds in arc per year, 
carries this point westward among the stars one sign, or 30 degrees, in about 2150 
years, so that stars on the ecliptic increase two hours in Right Ascension in about 
2150 years. But Hamal is not on the ecliptic and the nautical almanac gives its 
animal variation 3.3685 seconds, so that it increases two hours in Right Ascension 
in 2137 years. Hence about 2137 years ago, or BC. 250, the modern First point of 
Aries coincided with Hamal. And Hamal is certainly in the constellation Aries if 
it be not the ancient first point of Aries. The British Association Catalogue gives 
the right ascension of Hamal, or a Arietis, in 1850 as 1 h. .58 m. .43.58 sec, and 
Annual Precession 3.348 seconds. This would make a small difference, but not 
enough to affect the general result. 

(27). As to the remark, that: "the numerous records of eclipses, incorporated 
in this systematic astronomy, implied an enormous antiquity for the star-gazing 
Chaldeans." Professor Renwick, in his lectures to the Class of 1824 in Col. Coll., 
New York, referred to these eclipses in substance thus, according to my recollec- 
tion. 

(2§). The scientists who accompanied Napoleon in his Eastern expedition found 
a Chaldean account of their own nation, which carried its origin back to an im- 
mense antiquity, to a period called Kali Yug when all the planets were in a direct 
line from the sun. And in tracing down the national history they frequently re- 
ferred to eclipses. 

(29). This being reported, and the eclipses agreeing with calculation, produced 
consternation among those who had believed the Mosaic account. This was only 
partially removed by the thought that eclipses could be calculated backwards as 
well as forwards. 

(30). Now, go back to the Second School of Plato. They had investigated the 
curves of the Conic Sections. These were simply mathematical curiosities until 
the time of Newton. He found that these curves agreed precisely with the laws of 
gravity which he had investigated. And his laws of gravity explained the move- 
ments of all the heavenly bodies except that of the moon, and he laid his work aside 
as defective. 

(31). Then, there was no certainty that the measures of length, capacity, and 
weight had remained unchanged. Some unchangeable measure in nature was 
sought. The English proposed to make the standard of length, the pendulum 
beating seconds at a certain latitude. The French measured an arc of the meridian 
of the earth, and carried on a simultaneous trigonometrical survey for distance, and 
astronomical observations for latitude. Having passed a mountain, they found that 
the change in latitude made the earth smaller than they knew it to be. They re- 
peated their work to find the error, but with the same result. They then recognized 
the fact, that the error was caused by the attraction of the mountain. 

6 



KB. NOTES. 

(32). This having been made known, an English and a French astronomer made 
independent observations as to the attraction of mountains, with the same results 
that the weight of the earth is about five times as great as an equal bulk of water. 

(33). From the weight of the earth, the weight of each body in the solar system 
has been determined. The measure of the earth proved that it was larger than 
Newton had assumed it to be. He corrected this error, and his laws of gravity ex- 
plained the movements of all the heavenly bodies, and they were given to the pub- 
lic. These explain the irregularities in the movements of the planets, the attraction 
of one sometimes retarding, sometimes accelerating the movement of the other. 
And since this lecture was delivered, the accuracy of modern astronomical knowl- 
edge has been proved, by Leverrier's discovery of the most distant planet in our 
system, by calculating the size and position of a planet, that would account for the 
observed irregularity of the most distant planet that was then known. 

(34). Now, said Professor Renwick, when these modern discoveries are applied 
to these Chaldean statements, it is found that the planets were scattered through the 
heavens at the time that the Chaldeans state that they were all in a direct line from 
the sun, and that the eclipses did not fall at the times they state, and these once 
celebrated eclipses are now acknowledged by all to be fictitious. 

(35). As to the cuneiform inscriptions : These, when deciphered, may be found 
to be the same as the above Chaldean statements, or something similar. But in the 
above, there is no astronomic proof that Archbishop Ussher errs in giving BC. 
2349 as the date of the Flood, in accordance with the Mosaic account. (20.) 

(38). Jarvis (p. 18), after many quotations from ancient authors to prove that 
the Olympiads began JP. 3938=B.C. 776, says: "From the first Olympiad of 
Iphitus only, does profane history derive its definite form, and detach itself entirely 
from traditional conjecture." And Petavius calls this the "torch-light of ancient 
history." (OE. Notes.) 

(37). Newton's Chronology, London, 1725 (p. 80), says that the Thebans deter- 
mined the length of the solar year by the heliacal rising of the stars, and added 5 
days to the previous year of 12 months of 30 days. " This being at length prop- 
agated into Chaldea gave occasion for the year of Nabonassar .... This year was re 
ceived by the Persian empire from the Babylonians. And the Greeks also used it 
in the Era Philippcea, dated from the death of Alexander the Great. And Julius 
Caesar corrected it by adding one day in every 4 years " (p. 81). The 5 days were 
added by the last king of the shepherds (p. 82). Eudoxos, 60 years after Meton, in 
describing the sphere of the ancients, placed the solstices and equinoxes in the mid- 
dle of the constellations Aries, Cancer, Chelee, and Capricorn (p. 84). The first 
Greek sphere was for the Argonauts, and the names of the constellations are Argo- 
nautic (p. 86). In 1689 the equinox had receded 36 degrees, 44 minutes, since the 
Argonautic expedition (p. 87). This puts the expedition about 25 years after the 
death of Solomon (p. 93). Hipparchus discovered the precession of the equinoxes 
about one degree in 100 years, between NE. 586 and 618. The middle year, NE. 
602, is 286 years after Meton. (19-21.) 

(3§). This statement by Newton, that Eudoxos puts the equinox about the mid- 
dle of Aries shows that the zodiac, as described by Eudoxos, was constructed about 
BC. 1320, and not BC. 2350. (21-35.) 



jsts. 

PKEEACE. 

NS.=NEW ST YLE= GREGORIAN CALENDAR. 



The origin of NS. is given in AC. Notes 1-16. Its departures from the Nicean 
rule in AC. Examples 1st, 2d, 3d, and in AC. Notes 40, 48-51, 66-70, 72, 73, 78- 
80, 89-91, 123, and Authors in AC. Note 132, and HC. Notes, at the beginning. 

Explanations. 

The stereotype plates of the edition of 1874 are used in this edition for AM. ; 
GND. and Epacts ; NC; NS.; NS. Notes; OS.; and Scale. But the papers on 
AC; AC. Notes; HC; HCM., HC Notes; and JE.; have been extended, and 
some of the symbols have been changed. Therefore in these pages of 1874, in this 
edition, read 

AC. numbers=AC without the numbers. 

AO. =HC ; and AOC =HCM. ; and NB. AO. =HC Notes without the numbers. 

AU.=JE., andAIL 

NB.=Notes respecting what follows NB. 

NB. GND. and Epacts=GND. and Epacts, as a separate paper in alphabetical 
order. 

NB. NC.=NC as a separate paper. 

NB. Scale= Scale as a separate paper. 

NS. 1, 2, etc.=NS. Rule 1, 2, etc. 



















I*S. 
















(WS. I. 


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TABLE l.-Find by Table VI. 


or VII. t 


MOVEABLE FEASTS. 1 


n 

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13 




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13 


12 


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3 


Feb. 


1 


Feb. 18 


Apr. 5 


May 


10 


May 14 


May 24 


25 


Nov. 29l 


1875 


14 


23 


C 


2 


Jan. 


24 


" 10 


Mar. 28 


i< 


2 


6 


"* 16 


26 


•< 281 


1876 15 


4 


b. A 


5 


Feb. 


13 


Mar. 1 


Apr. 16 


t< 


21 


" 25 


June 4 


24 


Dec. §■ 


1877 j 1G 


15 


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Jan. 


28 


Feb. 14 


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". 


6 


" 10 


May 20 


26 


M 


1878 1 17 


28 


F 


5 


Feb. 


17 


Mar. 6 


" 21 


f. 


28 


" 30 


June 9 


23 


1 


1879 1 IS 


7 


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4 


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Nov. 3« 


1880 19 


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Jan 


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Mar. 28 


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May 16 


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1881 


1 





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Mar. 2 


Apr. 17 


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June 5 


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1882 


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4 


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Feb. 22 


9 


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May 28 


25 


Dec. 3fl 


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22 


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Jan. 


21 


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Mar. 25 


Anr. 


29 


3 


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27 


2l 


1881 


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f. E 


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Feb. 


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Apr. 13 


May 


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June 1 


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Nov. 39 


1885 


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1880 


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June 3 


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1887 


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Feb. 23 


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May 19 


May 29 


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Jan. 


29 


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" 10 


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26 


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1889 


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Feb. 


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Mar. 6 


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June 9 


23 


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1891 


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Mar. 29 


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1893 


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Feb. 15 


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Mav 21 


26 


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1894 14 


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Mar. 25 


Apr. 


29 


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27 


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1895 1 15 


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Feb. 


10 


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Apr. 14 


May 


19 


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June 2 


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1898 i 16 


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Apr. 15 


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1914 j 15 ! 3 


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1918 


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1920 


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1921 


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23 


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'•'■ 5 


" 15 


26 


" 27 


1922 


4 


2 


A 


5 


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12 


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Apr. 16 


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June 4 


24 


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1923 


5 


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Jan. 


28 


i-eb. 14 


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26 


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1924 


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a. G 


4 


" 


5 


Feb. 22 


" 8 


« 


13 


" 17 


May 27 


25 


Dec. 2 


1929 


11 


19 


F 


2 


Jan. 


27 


" 13 


Mar. 31 


" 


5 


" 9 


•' 19 


28 


" 1 


19.il) 


12 





E 


5 


Feb. 


16 


Mar. 5 


Ar. 2) 


it 


25 




' 29 


June 8 


23 


Nov. 30 



Note.— Trinity Sunday is seven days after Whit-Sunday. 

2 





















TVS. 








* 












(im 2.) 


(1) TABLE ll.-To Find Table IV. 




o 
o fccw 


Si 

ft 


d 

02 

ad 

ft 


o 

02* 
ft 


1 * 

'.2 « 

U O 


o 

a §>§ 


15 

rs 

a 

02* 

ft 


d 
m 

CO 

ft 


d 

Hi 
ft 


to 

o 


! o 
o Six' 


1=1 

02" 

ft 


d 
02 

ft 


d 

Hi 

02* 
ft 


la 



O 

«n ° • 
C tr 'X 

-, S « 

£ es -a 


02 
ft 


d 
02 

02* 
ft 


d 

h] 

02' 
ft 




325 


24 










3500 


9 


25 




B 


5600 


17 








7700 


28 


56 


24 




1582 





10 


4 


B 


3600 


8 




11 




5700 


18 


41 






7800 


27 


57 




B 


1600 











3700 


9 


26 






5800 


18 


42 


18 




79G0 


28 


5S 






1700 


1 


11 






3800 


10 


27 






5', 00 


19 


43 




B 


8000 


27 


25 




1800 


1 


12 


5 




3900 


10 


28 


12 


B 


6000 


19 








81 CO 


28 


59 






1900 


2 


13 




B 


4000 


10 








6100 


19 


44 


19 




8200 


29 


60 




B 


2300 


2 








41C0 


11 


29 






6200 


20 


45 






8800 


29 


61 


26 




2100 


2 


14 


6 




4200 


12 


30 






6300 


21 


46 




B 


8400 


29 








2-00 


3 


15 






4800 


12 


31 


13 


B 


6400 


20 




20 




8500 





62 






2300 


4 


16 




B 


4400 


12 








6500 


21 


47 














B 


2430 


3 




7 




4500 


13 


32 






6600 


22 


48 
















2500 


4 


17 






46 00 


13 


33 


14 




6700 


23 


49 
















20 


5 


18 






4700 


14 


34 




B 


6800 


22 




21 














2700 


5 


19 


8 


B 


4800 


14 








6900 


23 


50 














B 


2800 


5 








4900 


14 


35 


15 




7000 


24 


51 
















2900 


6 


20 






5000 


15 


36 






7100 


24 


52 


22 














30G0 


6 


21 


9 




5100 


ib- 


37 




B 


7200 


24 


















3100 


7 


22 




B 


5200 


is 




16 




7300 


25 


53 














B 


32 00 


7 








5300 


16 


38 






7400 


25 


54 


23 












3800 


7 


23 


10 




5400 


17 


89 






7500 


26 


55 














3400 


8 


24 






5500 


17 


40 


17 


B 


7600 


26 















(2). Memorized rales which incl-jde the Index (NS. 2% 21). (See NS. and AC. 2, 14, 15, 
16, 20, 21, 22, 24, 27 ; and AOC. 1 ; NI5. NS. 2, 16; 31 to 35 ; NB. Cal. 18—9, 10.) 

(3.) (!VB. NS. 1 to 7.) Table I. is not always given, but the rules to find these dates 
are always found in the Anglican Prayer Books and in the Roman Missal. 

Table II, is the Anglican Table II. wiih the addition of A D. 325, and 1582, and col- 
umns of NS. SC. and NS. LC. to illuslrate its construction by NS. 16. 

Table III. is the Anglican Table III with the addition of the column of Epaets to be 
used with Tabic VII. These are found by adding 13 days to the dates of the sitne 
Epaets for the Paschal New Moon in the Missal. This column, with the assistance of 
the Anglican Tables II., III., will, for all time, show the 30 changes of Epaets during 
each Great Cycle. The Missal gives two tables and 52 lines of printing for the single 
change of Epaets, here represented by the change from Index to 1, for Epaets from 
A D. 1582 to 1899, and refers to a nameless " book " for further information. Long 
(1266-8) gives three tables, here represented by Indexes 0, 1, 2 ; and says that Gavius 
gives 30 series of Epaets and tables up to A D. 303, 300. Delambre (V. 1, p. 18) says 
that Clavius gives 217 combinations. See Jarvis (p. 107) ; Wheatly (pp. 37-47) ; Rees 
(Cycle and Number ; Seabury (p. 201). For the memorized rule see (NS. 14). 

Table IV. is found in all the Anglican Prayer Books, except the day of March for the 
memorized rules to find the date of the Paschal Full Moon, by GN. and by Epaets (ITS. 
14); and the doub e dates April 17, 17, April 18, 18; and the Epaets, with Epact (25) 
extra which, in all cases, belongs ouly to GX 12 to 19 ; to illustrate NS. Retractions 

Table V. is found in works on the calendar, except that it is here shown to be per- 
petual by the mode of finding the centuries. 

Table VI is found in Anglican Prayer Book 5 *. 

Table VII. is copied from the Roman Missal, with slight modifications. 

The voluminous series of Greek Service Books and large Book of Rubrics, contain no 
part of the Russo-Greek Calendar. 
F 3 



NS. 



SOOOOOO-JCSaitf*. W-W KOOQ0<!O0)i^C0i.0KO©Q0<!©Ol^05t5K 



Day of Maich, 
NS. FGND. 






Day of the 
Month, Pas- 
chal, Full 
Moon. 



OOWtd>Q^HOCW>QtlBOOW^Q^KO^W^Q^HOO 



Sunday Letters, 



Epacts. 



~3 OS • OTrf^ CO to M-W 000<i05 0T^05tOK0005<iQ01iMWtOKO?OOD 



GO ~3 • OCTrf*.COeOl-»-©«DGO«*3CSClpP*.COeC M-W 50U0«3Q0l^05WH.Ol» 



o 



cototoeotototocototoi 



© © • oo ~j cs or >£*. co to 



CO tO • M- O O tt >? C5 Ct iMM K) ^9 0(»^OOJ^O;WH-0000«30(j(|^ 



to to • to to to 



CT rfi. . CO to 



OS GT • |^WMHOOOO<JOOl^WM i-J-t/ 000<jQCJI^WWKOOa)<i 



tO tO • tO tO tO tO tO CO Hi h* h-L >-■ p-i M- !->■ (-»■ 



-a os • WtMwtoKcoij5^0wT*>.05»KOffla)«?c50i^o:to p-^O 






CO^iQCl^OStOM-OCKXXiOOT^OSiO M-V^ OGO^CSOlrfi-COtO^O 



0000<JOSOlrf^COtO 1— W O00-aCS0l^C0t0H^OO00<JCiCTrf^C0t0 



©tOtOtOcOtOtOtOtOtOtO^I-^l-»-M-)-i-l-i-l-i-l-iV-i-v-i 
OO)^Q0ltMXMKOCDQ0<iOSl^C0WKOC0D<J050T^ 



WtOH-OtDOC^CSOllMWiO M>W «000«<{CSCyT^COcO'-^0000-qfOSOl 



to to to to to 



IV o-/ w w iv f- p- p- r— ■ r— • p— ■ p— ■ p— ■ i— - p- «■ >b. CO fO CO CO 

rf^COtOr^OOOO<JOSC?Ipfi-COCOI-^0000-505C7lpfi.COCO M-Q OOO^Ci 



I 



NS, 



( NS. 4. ) 


TABLE IV.- 


-To Find Easter from Table II. and III. 


IS 


1 1 

i — 

& 1 


m 
V 




p CO 


PHos 




<►.!*- 


«M * 


>> 


■ 


S3 JT*** 


S3 ^r*t 




o , 


O p3 


<a 




O gO 


5 go 








t3 

2 


o 
a 


2 S^ 


lis 




P^ 


ft 


02 


H 


O 


o 




21 


March 21 


c 


23 


14 




(1) Add one to the year A D., and divide the 


22 


" 22 


D 


22 


3 


14 




23 


" 23 


E 


21 




3 


sum by 19, and the remainder (if any) 


24 
25 


24 
" 25 


F 
G 


20 
19 


11 


11 


will be the Golden Number for that year. 


26 


" 26 


A 


18 


19 




If there be no remainder, then is 19 the 


27 


, " 27 


B 


17 


8 


19 




28 


" 28 


C 


16 




8 


Golden Number. 


29 


" 29 


D 


15 


16 






30 


" 30 


E 


14 


5 


16 




SI 


" 31 


F 


13 




5 


In Table V., find the Dominical for the year, 


32 

33 


April 1 
2 


G 
A 


12 

11 


13 

2 


13 


and in a Leap year, take the Dominical for dates 


34 
35 


3 

4 


B 

C 


10 
9 


10 


2 


after February 29, as indicated by its being a 


36 


5 


D 


8 




10 


capital letter. 


37 


6 


E 


7 


18 






38 


7 


F 


6 


7 


18 




39 


8 


G 


5 




7 


Then, in Table IV., find the date opposite to 


40 


9 


A 


4 


15 






41 


" 10 


B 


3 


4 


15 


the Golden Number, and the date next thereafter 


42 
43 


" 11 
" 12 


G 
D 


2 
1 


12 


4 


which has its Sunday letter the same as the Do- 


44 


" 13 


E 





1 


12 


minical, is Easter Sunday. 


45 


« !4 


F 


29 




1 




46 


" 15 


G 


28 


9 






47 


" 16 


A 


27 




9 


(2) To construct Table IV. Find in Table II. the 


48 


" 17 


B 


26 


17 








17 


B 


(25) 




17 


Index opposite to the beginning of the cen- 


49 


"• 18 

" 18 


C 
C 


25 

24 


6 


6 


tury in which Table IV. is to be used. Then 


50 _ 


" 19 
" 20 
" 21 

" .22 
" 23 


D 
E 
F 
G 
A 








in Table III. find this same Index under 

' each Golden Number, and opposite to its 

date, and Sunday letter, and Epact, which 




" 24 
" 25 


B 

c 








transfer from Table III. to Table IV. 



[3). 



Memorized rule 
21, 25 ; NB. 
AOC. 4. 



to find Easter for all time (NS. 11). (See NS. and AC. 2 to 15, 19, 20, 
NS. 2, 16 ; 31 to 35 ; and OS 1 to 3 , and AM. 3 ; and AG. 5, 6 ; and 



(srs. 5.) 



MS; 

TABLE V.-To Find NS. Dominical. 



(1) To find NS. Dominical: Divide 
the year A D. by 400. Then 
find the remaining hundreds of 
years in one of the fonr right 
hand columns, and in that col- 
umn, and opposite to the odd 
year, find the NS. Dominical for 
the whole of a common year, 
or the two Dominicals in a Leap 
year, of which the capital let- 
ter is for dates after February 29, 
and the small letter for dates be- 
fore February 29. 





1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

28 

27 

28 



Odd Tears. 



29 


57 


30 


58 


31 


59 


32 


60 


33 


61 


34 


62 


35 


63 


36 


64 


37 


65 


38 


66 


39 


67 


40 


68 


41 


69 


42 


70 


43 


71 


44 


72 


45 


73 


46 


74 


47 


75 


48 


76 


49 


77 


50 


78 


51 


79 


52 


80 


53 


81 


54 


82 


55 


83 


56 


84 



Hundreds of Years. 



100 2C0 



c 

B 
A 
G 
f. E 
D 
C 
B 

a. G 
F 
E 
D 

c. B 
A 
G 
F 

e. D 
C 
B 
A 

*•£ 

E 
D 
C 

b. A 
G 
F 
E 

d C 



E 
D 
C 
B 

a. G 
F 
E 
D 

c. B 
A 
G 
F 

e. D 
C 
B 
A 
F 
E 
D 
C 

b. A 
G 
F 
E 

d. C 
B 
A 
G 

f. E. 



300 



S 



G 
F 
E 
D 
B 
A 
G 
F 
D 
C 
B 
A 
F 
E 
D 
C 
A 
G 
F 
E 

d. C 
B 
A 
G 

f. E 
D 
C 
B 

a. G 



S 



b. 



b. A 
G 
F 
E 

d. C 
B 
A 
G 

f. E 
D 
C 
B 

a. G 
F 
E 
D 

c. B 
A 
G 
F 

e. D 
C 
B 
A 

g.F 
E 
D 
C 

b. A 



(2). Memorized rule for NS. Dominical (NS. 10). 
OS. 1 ; and AM. 3, 6. 



(See NS. and AC. 4, 5, 7, 10, 11, 13 ; and 



( STS. 6. ) TABLE Vl.-To Find Table I. from Tables IV. and V. 



u 

If 
el 


eptuagesima 
Sunday. 


P» 

2 * 


03 


a 

o 

O 


•a 

c 
5 


a 

.2 
'5 
a 

S3 
O 

OQ 


03 

ft 


>> 

03 

s 5 


a a 
•C «2 


is 


> 1 


n 


Oj 


<1 


Kl 


Ph 




< 




ts 


H 


w 


<1 


1 


Jan. 18 


F^b. 4 


Mar. 22 


Apr. 


26 


Apr. 


30 


May 10 


May 17 


27 


Nov. 29 


1 


19 


5 


" 23 


" 


27 


May 


1 


11 


" 18 


27 


30 


1 


20 


6 


24 


" 


28 


" 


2 


12 


19 


27 


Dec. 1 


2 


" 21 


7 


25 


c( 


29 


" 


p 


13 


" 20 


27 


2 


2 


' 22 


8 


26 


<( 


30 


(< 


4 


14 


21 


27 


3 


2 


23 


9 


27 


May 


1 


" 


5 


" 15 


" 22 


26 


Nov. 27 


2 


24 


10 


" 28 


" 


2 


" 


6 


16 


" 23 


26 


28 


2 


" 25 


" 11 


29 


<i 


3 


<< 


7 


17 


24 


26 


29 


2 


." 26 


12 


30 


« 


4 


tt 


8 


18 


" 25 


26 


30 


2 


'« 27 


13 


•' 31 


« 


5 


« 


9 


19 


" 26 


26 


Dec. 1 


3 


" 28 


14 


Apr. 1 


" 


6 


" 


10 


20 


" 27 


26 


2 


3 


" 29 


15 


2 


<< 


7 


" 


11 


21 


" 28 


26 


3 


3 


" 30 


16 


3 


<< 


8 


tt 


12 


22 


" 29 


25 


Nov. 27 


3 


" 31 


17 


4 


<« 


9 


'* 


13 


23 


" 30 


25 


" 28 


3 


Feb. 1 


18 


5 


" 


10 


" 


14 


24 


" 31 


25 


" 29 


3 


2 


19 


6 


<< 


11 


<< 


15 


25 


June 1 


25 


30 


3 


3 


20 


7 


(< 


12 


" 


16 


" 26 


2 


25 


Dec. 1 


4 


4 


21 


8 


<( 


13 


it 


17 


27 


3 


25 


2 


4 


5 


22 


9 


« 


14 


" 


18 


28 


4 


25 


3 


4 


6 


23 


10 


<« 


15 


tt 


19 


29 


5 


24 


Nov. 27 


4 


7 


24 


11 


" 


16 


tt 


20 


30 


6 


24 


28 


4 


8 


25 


12 


" 


17 


" 


21 


31 


7 


24 


- 29 


4 


9 


26 


13 


" 


18 


" 


22 


June 1 


8 


24 


30 


4 


" 10 


27 


" 14 


(i 


19 


" 


23 


2 


9 


24 


Dec. 1 


6 


11 


" 28 


" 15 


« 


20 


" 


24 


3 


10 


24 


" 2 


5 


12 


Mar. 1 


16 


" 


21 


tt 


25 


4 


- 11 


24 


3 


5 


13 


2 


17 


" 


22 


n 


26 


5 


" 12 


23 


Nov. 27 


5 


" 14 


3 


18 


" 


23 


tt 


27 


6 


" 13 


23 


28 


5 


" 15 


4 


" 19 


u 


24 


a 


28 


7 


" 14 


23 


" 29 


5 


16 


5 


" 20 


" 


25 


tt 


29 


8 


" 15 


23 


" 30 


5 


u 1? 


6 


" 21 


" 


26 


a 


30 


9 


16 


23 


Dec. 1 


6 


18 


7 


22 


<( 


27 


a 


31 


10 


tt 17 


23 


2 


6 


" 19 


8 


23 


" 


28 


June 


1 


" 11 


" 18 


23 


3 


6 


20 


9 


24 


" 


29 


it 


2 


12 


" 19 


22 


Nov. 27 


6 


21 


10 


25 


" 


30 


" 


3 


13 


20 


22 


" 28 



' v 2). Find the date of Easter by Table IV. Then, in Table VI., find the same date of Easter, 
and opposite to that date find all the dates in Table I. ; except in a Leap Year, add one 
day to dates before March 1, and take the number of Sundays after Epiphany, 
as if Easter fell one day later than its actual date. 

(3). Memorized rules for those dates (NS. 11, 25). (See NS. and AC. 1 to 7 ; 9 to 15, 23, 25; 
and OS. 2, 5; and AM. 3, 4, 5; and AO. 5 ; and AOG. 4 ; and NB. NS. 



( rVS. 7.) TABLE VII.-To Find the Dates in Table I., from Table IV. and V, 



^ 
•S 






c3 

s 


t 


•Jl 


63 


.2 


1 


-Si II 


"3 

a 

o 


Table of Epacts. 


£3 


1 


02 




<o a 
1 oa 


S A 


£5 02 




•5 & 


A 




02 


02 




< 


H 


<5 


rjl 






23 


1 


Jan. 


18 


Feb. 4 


Mar. 22 


Apr. 30 


Mny 10 


27 


Nov. 29 




22, 21, 20, 19, 18, 17, 16 


2 


" 


25 


" 11 


" 29 


May 7 


" 17 


26 


" 


D 


15, 14, 18, 12, 11, 10, 9 


3 


Feb 


1 


" IS 


Apr. 5 


•' 14 


" 24 


25 


" 




8, 7, 6, 5, 4, 8, 2 


4 


" 


8 


" 25 


" 12 


" 21 


" 31 


24 


" 




1, 0, 29, 28, 27, 26, (25) 25, 24 


5 


" 


15 


Mar. 4 


" 19 


" 28 


June 7 


23 






23,22 


1 


Jan. 


19 


Feb. 5 


Mar. 23 


May 1 


May 11 


27 


Nov. 30 




21, 20, 19, 18, 17, 16, 15 


2 


" 


26 


" 12 


" 30 


" 8 


" 18 


26 


" 


E 


14, 13, 12, 11, 10, 9, 8 


3 


Feb. 


2 


" 19 


Apr. 6 


" 15 


" 25 


25 


" 




7, 6, 5, 4, 3, 2, 1 


4 


tt 


9 


" 26 


" 13 


" 22 


June 1 


24 


k 




0, 29, 28. 27, 26 (25), 25, 24 


5 


a 


16 


Mar. 5 


" 20 


" 29 


" 8 


23 


" 




23, 22, 21 


1 


Jan. 


20 


Feb. 6 


Mar. 24 


May 2 


May 12 


27 


Dec. 1 




20, 19, 18, 17, 16, 15, 14 


2 


" 


27 


" 13 


" 31 


" 9 


" 19 


26 


<< 


F 


13, 12, 11, 10, 9, 8, 7 


3 


Feb. 


3 


" 20 


Apr. 7 


" 16 


" 26 


25 


« 




6, 5. 4, 3. 2, 1, 


4 


<( 


10 


" 27 


" 14 


" 23 


June 2 


24 


« 




29, 28, 27, 26 (25), 25, 24 


5 


" 


17 


Mar. 6 


" 21 


" 30 


" 9 


23 


" 




23, 22, 21, 20 


2 


Jan. 


21 


Feb. 7 


Mar. 25 


May 3 


May 13 


27 


Dec. 2 




19, 18, 17, 16, 15, 14, 13 


3 


" 


28 


" 14 


Apr. 1 


" 10 


" 20 


26 


(< 


G 


12, 11, 10, 9, 8, 7, 6 


4 


Feb. 


4 


" 21 


" 8 


" 17 


" 27 


25 


n 




5, 4, 3, 2, 1, 0, 29 


5 


" 


11 


" 28 


" 15 


" 24 


June 3 


24 


" 




28, 27, 28 (25), 25, 24 


6 


" 


18 


Mar. 7 


" 22 


" 31 


" JO 


23 


" 




23, 22, 21, 29, 19 


2 


Jan. 


22 


Feb. 8 


Mar. 26 


May 4 


May 14 


27 


Dec. 3 




18, 17, 16, 15, 14, 13, 12 


3 


" 


29 


" 15 


Apr. 2 


" 11 


" 21 


26 


,< 


A 


11, 10, 9, 8, 7, 6, 5 


4 


Feb. 


5 


" 22 


" 9 


" 18 


" 28 


25 


" 




4, 3, 2, 1, 0, 29, 28 


5 


•' 


12 


Mar. 1 


" 16 


" 25 


June 4 


24 


" 




27, 26 (25), 25, 24 


6 


" 


19 


" 8 


" 23 


June 1 


" 11 


23 


" 




23, 22, 21, 20, 19, 18 


2 


Jan. 


23 


Feb. 9 


Mar. 27 


May 5 


May 15 


26 


Nov. 27 




17, 16, 15, 14. 13, 12, 11 


3 


<i 


30 


" 16 


Apr. 3 


" 12 


" 22 


25 


" 


B 


10, 9, 8, 7, 6, 5, 4 


4 


Feb. 


6 


" 23 


" 10 


" 19 


" 29 


24 


« 




3, 2, 1, 0. 29, 28, 27 


5 


« 


13 


Mar. 2 


" 17 


•« 26 


June 5 


23 


(< 




26 (25), 25, 24 


6 


" 


20 


" 9 


" 24 


June 2 


" 12 


22 


« 




23, 22, 21, 20, 19, 18, 17 


2 


Jan. 


24 


Feb. 10 


Mar. 28 


May 6 


Mav 16 


26 


Nov. 28 




16. 15, 14, 13, 12, 11, 10 


3 


" 


31 


" 17 


Apr. 4 


- 13 


" 23 


25 


" 


C 


9, 8, 7, 6, 5, 4, 3 


4 


Feb. 


7 


« 24 


" 11 


" 20 


" 30 


24 


t< 




2, 1, 0, 29, 28, 27, 26 (25) 


5 


" 


14 


Mar. 3 


" 18 


" 27 


June 6 


23 


« 




25,24 


6 


« 


21 


" 10 


" 25 


June 3 


" 13 


22 


it 



Note.— Trinity Sunday is seven days after Whit-Sunday. 
" Rogation Sunday is four days before Ascension. 



(2). In Table IV. find the Epact opposite to the Golden Number of the year. In Table V. find the 
Dominical for the whole of a common year, or for dates after February 29 in a Leap Tear, 
as indicated by its being a capital letter. Then in Table VII. find the Epacfc concurring 
with the Dominical, and on the same line as the Epact, find the dates in Table I. ; except 
in a Leap Year, add one day to all dates before March 1, and take the number of Sundays 
after Epiphany as if Easter fell one day later than its actual date. 

(3). Memorized rules to find these dates (NS. 11, 25). (See NS. and AC. 1 to 7, 9 to 15, 23, 25; 
NB. NS. ; and OS. 2, 5 ; and AM. 3, 4, 5 ; and AO. 5 ; and AOC. 4.) 



8 



Memorized and verbal rules, witli examples in common almanacs (NS. 8 to 29), 
Explanations (NB. NS.), Contradictions (NB. NS.,31 to 35), (NB. Authors). 

§. CIKCEE (A. Circle). 

9. CYCLE. For the yearJP. add 4713 to the year AD. Then divide the 
year JP. by the Circle 19 for GN., or by the Circle 28 for Solar Cycle, or by the 
Circle 15 for Indiction, and the remainder is the year of the Cycle. 

10. DOMINICAL.. (1.) Remember the date of the first Sunday in the year, 
and that date, Jan. 1 to 7, gives the Dominical A. to G. for the whole of a common 
year ; or before Feb. 29 in a leap year, as marked in small letters (NS. 5, 10-4th). 
Then the next earlier letter is for dates after Feb. 29, counting G. as next before 
A., as marked with large letters in (NS. 5; 10 — 4). 

Thus A D. 1874, Sunday, Jan. 4 = D. for NS. Dominical. And every date which 
has its Sunday letter the same as the Dominical NS. or OS. or AC, is Sunday dated 
NS. or OS. or AC, according to the Dominical (NS. and AC, 1, 4, 5, 7, 10, 11, 13, 
29). 

(2.) For all time after (NS. 18). 

Divide the centuries by 4, and twice what does remain 
Take from 6, and to the number you gain 
Add the odd years and their fourth, which dividing by 7, 
What is left take from 7, and the letter is given. 

And 1 to 7 = A to G for dates after Feb. 29 in a leap year, as given in capital let- 
ters (NS. 5, 10-4th ; 23). 

(&) Or, to the number found for OS. Dominical by (OS. 1), add NS. SC. for NS. 
Dominical, or add AC SO. for AC Dominical, and divide the sum by the circle 7, 
and the remainder 1 to 7 will be A to G for dates after Feb. 29 in a leap year (NS. 
and AC 8, 27). 

(4) Or, from A D. 1700 to March 1, A D. 1900, find the year of the Solar Cycle 
(NS. 9). Then find the same number in the following NS. Solar Cycle, and opposite 
to that number find N S. Dominical, with small letters for dates before Feb. 29 in a 
leap year. 



1 € 


. D 


5 f 


f. F 


9 b. 


A 


13 d. 


C 


17 f. 


E 


21 a. 


G 


25 c 


5. B 


2 


C 


6 


E 


10 


G 


14 


B 


18 


D 


22 


F 


26 


A 


3 


B 


7 


D 


11 


F 


15 


A 


19 


C 


23 


E 


27 


G 


4 


A 


8 


Q 


12 


E 


16 


G 


20 


B 


24 


D 


28 


F 



(5.) Or, for all time after (NS. 18), to memorize this table and its modifications, 
add one day to NS. SC. (NS. 27), and divide the sum by the circle 7 (NS. 8), and the 
remainder 1 to 7 = A to G- for the year 28. Then, as above, write down the Do- 
minicals in the reverse order of the dates, doubling the letters in the leap years 
25, 21, 17, 13, 9, 5, 1. Thus 1 + 12, NS. SC. =*= 13 ;-4-7, leaves 6 = F for year 28 in the 
table above. Do the same with AC. SC. for Dominical AC. 

11. EASTER. Find NS. FGND. and NS. Ferial for that date. The Sunday 
next thereafter is NS. Easter (NS. 1, 4, 7, 9, 11, 13, 14, 15). For <)<. Easter, see 
(AM. 1 to 7 ; OS. 1 to 5). 

9 



ITS, 



12. EPACT, for the year. Multiply GN. by 11, and add the product to the Key 
epact, and divide the sum by 30 and the remainder =*NS. Epact (NS. 1, 3, 4, 9, 12, 
14, 15, 21). 

13. FJE RIAL., or day of the week. (1.) Find the Sunday letter for the 1,8, 15, 
22, 29 of each of the twelve months, the same as the initial letter of the following 
12 words ; 

At, Dover, Dwells, George, Brown, Esquire, 
Good,. Christian, Fitch, And,- David, Friar. 

Then find the Dominical (NS. or OS. or AC). Then count the Sunday letters for- 
ward from the Dominical as Sunday ,-to the Sunday letter as found for the 1, 8, 15, 
22, 29th of the month, and thus find the Ferial for these dates, and thence any in- 
termediate ferial dated OS. or NS. or AC, according to the Dominical (NS. and AC, 
1, 4, 7, 10, 11, 13,) (OS. 3 ; AM. 6). 

(2.) Examples (AM. 7) for OS. Ferials and (NS. 1) for NS. Ferials. Also : Find 
the Dominical (N£. or OS., or AC.) Then, in the following table, find at the head of 
one of the columns, the Sunday Letter the same as the Dominical, and under that 
letter find the date of every Sunday in a common year, or in that part of a Leap 
Tear which corresponds with the Dominical, and dated NS. or OS., or AC, accord- 
ing to the Dominical. 

Also, in this table, find the Sunday Letter for each day in the year, excepting 
Feb. 29, which has no letter. 

Also find the Sunday Letters for the 1, 8, 15, 22, and 29th of each of the twelve 
months (NS. 13-1). 



Months. 


Sunday Letters. 


Months. 


Sunday Letters-. 




A 


B 


C 


D 


E 


F 


G 




A 


B 


C 


D 


E 


F 


G 


January 


1 


2 


3 


4 


5 


6 


7 








1 


2 


3 


4 


5 




8 


9 


10 


11 


13 


13 


14 


August 


6 


7 


8 


9 


10 


11 


12 


October 


15 


16 


17 


18 


19 


20 


21 




13 


14 


15 


16 


17 


18 


19 




22 


23 


24 


25 


26 


27 


28 




20 


21 


22 


23 


24 


25 


2ft 




29 


30 


31 












27 


28 


29 


30 


31 


1 






1 


2 


3 


4 














2 


February 


5 


G 


7 


8 


9 


10 


11 




3 


4 


5 


6 


7 


8 


9 


March 


12 


13 


14 


15 


16 


17 


18 


September 


10 


11 


12 


13 


14 


15 


16 




19 


20 21 


22 


23 


24 


25 


December 


17 


18 


19 


20 


21 


22 


23 


November 


26 


27 28 


29 


30 


31 


— 




24 

31 


25 


26 


27 


28 


29 


30 




2 


3 


4 


5 


6 


7 


1 

8 




— 


1 


2 


3 


4 


5 




April 




6 


July 


9 


10 


11 


12 


13 


14 


15 




7 


8 


9 


10 


11 


12 


13 




16 


17 


18 


19 


20 


21 


22 


May 


14 


15 


16 


17 


18 


19 


20 




23 


24 


25 


26 


27 


28 


29 




21 


22 


23 


24 


25 


26 


27 




30 


31 














28 


29 


30 


31 


1 


2 


























3 






June 


4 


5 


6 


7 


8 


9 


10 








11 


12 


13 


14 


15 


16 


17 








18 


19 


20 


21 


22 


23 


24 




















25 


26 


27 


28 


29 


30 





10 



KB, 

14. FG^i D = Full Moon = 14th Nisan from AD. 1700 to 1899. (1.) Multiply 
GN. by 11 ; divide the product by 30 ; subtract the remainder from the Key 
date (March 53 until AD. 1900), and the second remainder is the date of NS. Full 
moon by scale, if on or between March 21 and 50. If not, then add or subtract 
30 days to bring it there. 

(2.) Or, subtract the NS. Epact from January 103 or March 44, and the remain- 
der is the date by scale, if on or between March 21 and 50. If not, then add or 
subtract 30 days to bring it there, (as from AD. 1700 to 1899.) 

(3.) For all time after (NS. 18), find the date as above. Then, if any date thus 
fall on March 50, retract it to March 49 (April 18), and if the date of any GN. from 
GN. 12 to 19 thus fall on March 49, retract it to March 48 (April 17). And in all 
cases, if the date exceed March 31, subtract 31, and call the remainder April. 
(NS 4, 7, 11, 14.) 

(4.) Examples. Every date in (NS. 3, 4), and in (AC. 3, 4 when NS. 14—3 is 
omitted). 

15. Oft. = Golden Number (NS. and AC. 3, 4, 9, 15 ; NB. GND. ;) (AM. 2 ; OS. 2). 

16. INDEX. (1.) This is memorized in combination (NS. 20, 21). 

(2.) For all time after (NS. 18). To the constant 24 add NS. SC. ; from the sum 
subtract NS. LC. ,• divide the remainder by 30, and the second remainder = NS. 
Index (NS. 2, 22, 27 ; AC. 16.) 

(3.) To tabulate NS. 2, count Index = in AD. 1582 or 1600, then add one day 
for each centurial year that is not marked " B " (for Leap Year), and from the sum 
subtract one day in each centurial year when NS. LC. increases one day, until the 
result be 30 days or more. Then subtract 30 days. 

IT. INDICTION. (NB. Indiction.) 

18. INTRODUCTION. Count all recorded dates as OS. (AM. 3, OS. 3, 4), 
until the introduction of NS., when 10 days NS. SC. were added to Oct. 5, 
making- Oct. 5-15, AD. 1582, in Rome, Spain, Portugal ; Dec. 10-20, AD. 1582, in 
Brabant, Flanders, Hainault ; Dec. 15-25, AD. 1583, in France ; AD. 1585, in the 
Romish provinces of Germany ; AD. 1586 in Poland ; AD. 1587 in Hungary ; Sept. 
4-15, AD. 1752, in England and colonies; AD. 1778 in Prussia. (See Brady, pp. 28, 
29 ; Jarvis, pp. 95, 96 ; Long, § 1244 ; Adams, pp. 354-5 ; Wheatly, 37-8 ; Renwick- 
Calendar ; Rees-Calendar.) 

19. JP. To find the year JP. (Julian Period) add 4713 to the year AD., or sub- 
tract the year BC. from 4714 (NB. JP.) 

20. KEV DATJE = March 55 from AD. 1800, March 1 ; to AD. 1900, March 
1. (NS. and AC. 14 ; OS. 2). 

(2). For all time. To March 54 add the NS. Index for the century and the sum 
=. Key date. Examples as for (NS. and AC. 14) ; (NS. and AC. 16.) 

If more convenient, subtract 30 days. Thus AD. 8200 to AD. 8399. Key date 
March 83-30 = March 53. 

(3.) Or, multiply any GN by 11, divide the product by 30 ; add the remainder to 
GND and the sum = key date for the whole series, if by scale. 

21 KEY EPACT (1.) = 19 from AD. 1700, March 1, to AD. 1900, March 1. 

(2.) For all time, subtract the NS. index from 20 (increased by 30 if required), and 
the remainder = Key epact. (Examples as for NS. 14) (NS. and AC. 16.) 

22. liC. = Lunar Correction. (1.) Memorize in combination (NS. 14, 16, 20, 21). 

(2 ) For all time; count 4 days in AD. 1582, and thereafter subtract 18 from the 

11 



ire. 

centuries AD. ; divide the remainder by 25 for the first quotient ; divide the second 
remainder by 3 for the second quotient so that it be not more than 7. Then multi- 
ply the first quotient by 8, and to the product add the second quotient and the 
constant 5, and the sum == NS. LC. 

(2). Or begin with 5 days in AD. 1800 and add one for each 300 years seven 
times, and then in 400 years once, making* 8 days in 2500 years, and repeat (NS 
and AC. 2, 16). 

23. LEAP TEAR, (1.) Divide by 4 the odd years, omitting the centuries, and 
if there be no remainder, the year is a leap year (NS., OS. and AC.) Divide by 4 the 
centuries, omitting the odd years, and if there be no remainder, the centurial year 
is NS. Leap Year marked B in (NS. 2). All other years are common years by NS. 
But all centurial years are leap years by OS. And this difference = NS. SC. (NS. 
27.) 

24. MARCH 21 is the assumed date of the Vernal equinox by "Paschal 
Canon." It was its artificial maximum Julian date in AD. 325, when its Calendar or 
actual date was March 20. Contra (NB. ISC.) 

25. MOVEABLE FEASTS, by memory. Find the Dominical and the 

date of Easter. Then, 

Advent Sunday is Nov. 27, Sunday Letter B, when the Dominical is B, to Dec. 3 
«= letter A when Dominical is A. Then : 

Septuagesima \ ( nine \ 

Sexagesima ( gund . J eight ( week brf 

Quinquagesima f J seven f 

Quadragesima ) ( six ) 

Rogation Sunday ] ( five weeks \ 

S5 ? «■ f i 3 ls dayS « ft « »— 

Trinity Sunday ) ( 8 weeks ) 

26. RETRACTIONS, memorized (NS. 14-3d). Examples (NS. 3, 4, 14, 26), 
(NB. NS. 3,14 ; NB. AC. 3,26.) 

27. SC. = For NS. Solar Correction (1) remember 12 days, from March 1, AD. 
1700, to March 1, AD. 1900, which add to dates OS. to find dates NS. ; and subtract 
from dates NS. to find dates OS. (2.) Also memorize in combination (NS. 16, 20, 
21). 

(3.) For all time after (NS. 18). Subtract 12 from the centuries AD.; divide 
the remainder by 4 for quotient and second remainder. Then multiply the quotient 
by 3, and to the product add the second remainder and the constant 7, and the sum 
«= NS. SC. 

(4.) Or, begin with 10 at AD. 1500, and add one day for each centurial year that 
is not NS. Leap Year (NS. and AC. 2, 16, 23). (NB. AC. 2-2.) 

28. SCALE. (NB. Scale). 

29. SUNDAY LETTERS. (NS. 3,4,13). 

30. TABLES. (NS. 1 to 7). 

12 



BjTS. l\OTES. 

1 to 7. These are transferred to (NS. 2— 3d). 

CONSTRUCTION OF TABLES II. AND III. 

2, 16. For Table II., set down in tabular form the quantities found by (NS. 16). 

3, 14—1, 2. For Table III., prepare a blank table, with the upper line of NS. (IN., 
and a lower line of corresponding AM. GN., and with dates and Sunday letters car- 
ried down regularly to April 19, as in (AC, Table III). Then add 13 days to the 
Epacts for the Paschal new moon, as found in the Missal down to April 17th, and 
continue, as in AC, Table III., April 18 = C = 25, April 19 = D = 24. 

Then assume that GN. 3 falls on March 21, as the earliest limit (NS. 24), and 
from this standard— GN. 3 = March 21 — measure off by scale (NS. 28) the dates of all 
the other GN. in the series. Then, under each GN. and opposite to its date thus found 
place the same index " 0." Then, in each column, set down the indexes 1 to 29 in 
the circle of 30 days on or between March 21 and April 19, beginning next after, 
and ending next before the index " 0" This completes Table III., in accordance 
with the memorized rule (NS. 14— 1st, 2d) and (AC. 3, 26). 

14 — 3. Then retract all the indexes which by scale fall on April 19 to second April 
18, and carry with them their Epact 24 ; thus doubling it with 25 at April 18. Then 
retract the indexes of all GN. from GN. 12 to 19, from April 18 to second April 17, 
and carry with them their epact (25), marked extra to show that it only belongs to 
GN. 12 to 19, and thus double 26 regular with (25) extra. This completes Table III., 
in accordance with (NS. 2, 3, 4, 7, 14). 

EXPLANATION OF TABLE II. 

2, 16. In Table II., the index to 29, is the number of days after March 21 
(NS. 24) on which falls the standard full moon for the 14th Nisan in the year GN. 3. 
It assumes that, in A D. 325 = GN. 3 = the year of the Council of Nicea, this 
moon fell 24 days after March 21, and, calculating in Julian years of 363.25 days, 
this moon, returning in each 19 years, had receded 4 days in A D. 1582 and 5 days in 
A D. 1800. and will continue to recede one day in 300 years seven times, and then 
in 400 years once ; making 8 days in 2500 years = 0.32 day per century = NS. LC. 

(NS. 22).. 

But a mean year of 365.242,216 days is actually 0.007,784 days shorter than a 
Julian year of 365.25 days. 

The index assumes that it is 0.007,500 days shorter, and hence March 21 in Julian 
time or (OS.) had advanced towards the summer solstice 10 days in A D. 1582, 
or, in other words, the mean date of the vernal equinox, counted in Julian years, had 
receded 10 days in A D. 1583, and 11 days in A D. 1700, and will continue to recede 
3 days in 4 centuries = 0.75 day per century — NC. SC. (NS. 2, 24, 27 ; AC 2, 24, 

27). 

Hence, while in terms of OS. the moon recedes at the rate of 0.32 day per cen- 
tury, the vernal equinox recedes at the rate of 0.75 day per century, and thus the 
moon recedes 0.43 day per century less than the equinox ; and, assuming that NS. SC. 
will keep March 21, NS., up to the actual date of the vernal equinox, the moon 
GN. 3 will advance towards the summer solsiice at the rate of 0.43 day per cen- 
tury. 

This caused the moon GN. 3 to advance from 24 days after March 21 in A D. 325 
(== constant 24 in NS. 16) to 30 days in AD. 1582 in equinoxial time, when the 

13 



NS. 1VOTES. 

moon 30 days earlier in the same standard year fell at the index " " days after 
March 21, NS., and this second moon became the standard for the second and pres- 
ent Great Cycle beginning in A D. 1582 and ending A D. 8500, when, in like man- 
ner, the moon 30 days earlier in the same year GN. 3 will become the standard for 
the next and third Great Cycle. 

This moon, advancing at the rate of 0.43 day per century, makes the average 
Great Cycle 6977 years in which to advance 30 days (= 30-5-0.0043). But NS. LG. 
and NS. SC. being in whole days, and NS. LC. only applied at the end of 3 and 4 
centuries, the present Great Cycle extends from A D. 1582 to A. D. 8500 = 6918 
years (NB. AC. ; NB. Calendars). 

EXPLANATION OF TABLE III. 

3, 14. This Table III. is given in full in the memorized rules (NS. 14), excepting 
the Greek GN. To memorize Table III. with Greek GN, add 3 in a circle of 19 to 
convert GN. AM. into GN. J.P., and then proceed as iu NS. (AM. 2, 4 ; NS. 8, 9 ; 
NB. scale 7.) 

This Table III. is a collection of Scales to measure the dates of the whole series 
from the varying dates of the standard GN. 3. Before the retractions (NS. 14 — 3d), 
the mass of figures under the 19 GN. show, that, for every day that GN. 3 advances, 
each other GN. must advance one day in the circle of 30 days on and between March 
21 and April 19, in order to preserve the Scale unbroken, until GN. 3 has run its 
course of 30 days after March 21, and a new GN. 3 takes its place at days after 
March 21, when all GN. fall on the same dates as at the beginning of the previous 
or of any other great cycle. And each GN. takes its moon 30 days earlier in the 
same year GN., when its index passes from April 19 to March 21. 

The retractions from Apr 1 19 to second April 18 keep the dates within the " Pas- 
chal limits = March 21 and April 18." This forces back GN. 12 to 19 when GN. 1 
to 8 are retracted, to prevent two moons in the same series falling on the same date, 
because, by scale, GN. 1 to 8 fall on the day next after GN. 12 to 19, without a va- 
cant date between them. This necessarily occurs when GN. 12 to 19 fall on April 
18. Hence (NS. 14— 3d.) (NB. AC.) 

(NB. Am hors.) Jarvis (pp. 95, 96, 105-110); Lon- (1244-1273) ; Brady (38-29) ; 
Adams (354-355); Wheatly (34-37); Renwick (calendar); Rees (calendar, cycle 
number); Monravieff (Vol. 1, pp. 355-6); Montuclai Vol. 1, p. 582^; Delambre (Vol. 1, 
p. 1 2) says " I found the calendar better than its authors supposed. " Long (1267) says 
that. Clavius explains the system and defends it from the attacks of Mcestlinus.Vieta 
and Scaliger. The Missal (Be festibus Mobilibus) says : " Be qua re plura inveniea 
in libro nova; rationis resiituendi Kalendarii llomani" Barnard ; Gauss ; Blunt ; 
Neale. (AC. Notes 131, 132.) 

CONTRADICTIONS. 

31. Seabury (NB. Authors) desires the Anglicans to " re-cast " their calendar and 
adopt the Roman mode (pp. xiv., x., xi., 117, 118, 236, 207). 

For this purpose he makes remarks on the following pages, which are placed 
among the Contras. 

On pp. 206, 7, 118, 211, he calls NS. Tables II. and III. " a wilderness of figures f 
while, without the present addition of Epacts, they form a better condensation of 
the entire system of NS. than can be found elsewhere. 

32. On pp. 197, xii., xiii., 124, 126, 131, 134, 152, 194, 198, he advocates * the symple 
and immutable system of Epacts," while the immutable Epacts are like Sunday let 

14 



NS. NOTES. 

fcers, and tlie Epacts which determine Easter are like Dominicals, and are derived 
from the GN. that are used by the Anglicans and change simultaneously 30 times 
during each Great Cycle. ; and of these changes the Missal gives but one, while the 
Anglican Table III. gives them for all time (NB. NS. 2; NB. GND. 8.) . 

33. On pp. 78, 67, 71, 72, 90, he says : u The Alexandrian Canon was founded on the 
Cycle of Meto (reduced from 6940 to 6939 day.% 18 hours)," and "drawn off with 
difficulty from the use of the Jewish Cyele of 84 years." Now, the Alexandrian 
Canon or Nicean Cycle of the century after A D. 325 (NC), and the Metonic Cycle 
of BC. 432 (OE.), and the present Jewish Cycle of A D. 360 (AO.) are fundamentally 
different. Neither is a copy of the other. Neither can be modified into the other. 
-The characteristic of the Nicean Cyele (NC. NGND. in NB. GND.) is the seale which 
counts 18 years of 365 days and one year of 366 days, making 6936 days. This 
always counts in Julian time, and is thereby expanded to 6939.75 days ; and it 
counts by whole days, and makes no difierenee between a eommon year and a leap 
year ; and begins the day at all hours of the natural day (NB. NC. Contra). The 
Metonie Cycle (OE.) also counts by whole days; but, when reduced to terms of J P. 
it counts 365 days in a common year and 366 days in a leap year, and begins the 
day invariably at midnight at Athens. The pres mt Jewish Cycle ( AO.) measures 
19 lunar years of 6 different lengths by 235 lunations, which vary from the latest 
determination only 5f seconds per year, and eounts invariably from 6 hours after 
noon at Jerusalem (or at Eden, says Muler), and, when reduced to Christian dates, 
makes a common year 365 and a leap year 366 days. 

34. On pp. 123, 194, xiv., 89, 189, 200, 211, he condemns the " Hanoverian method " 
of finding lunar dates by means of Golden Numbers. But this was begun by Meton 
and Euctemou about 2300 years back (OE.); (unless they borrowed it from the 
Egyptians or from the Babylonians, as may be suspected from their determination 
of the date of new moon and of the Summer Solstice in terms of NE.) This ha? 
been used by all Christians since A D. 534. It is now used by the Greek Church 
(AM.) It is now used by the Roman Church in the modified form of Epacts. (NS.12.) 

35. On p. 193, he says : " The Paschal Feast . . . was wrested from its connection 
and made to stand alone; as if the Church, wearied of God's own ordinance tor the 
regulation of her annual solemnities, wou'd choose some strange light, which should 
shine like the Dog star but for one month in the year" [sic]. Now the Dog star 
shines about eleven months, until overpowered by the light of the sun. And this 
change was made by Dionysius Exiguus, A D. 525 (Seabury, p. 78), and confirmed 
by the Council of Chalcedon, A D. 534, and from that day to the present the Pas- 
chal month alone has been used to find the date of Easter by all Christians without 
exception (AM. ; G-\ ; NS. 4; NS. 7). But, since the introduction of the Roman Cy- 
cle of BC. 45 (AU. GN), a variety of cycles of 235 moons have been constructed, 
fo lowing the receding dates of the moon in terms of OS., followed by the equivalent 
Cycle of Epaets in the Roman Miss »1 ; to answer imperfectly the purpose of a mod- 
ern almanae (NB. GND.) And such are now cut on walking sticks and used in 
the north of Europe, under the name of Clogs, Reinstocks, Rumstaffs, Runstocks, 
PaJmsteries, Seipiones, Runioi, Baeuli, Annales. Staves, Stakes (Brady, p. 47 ; Hones 
Preface : Rees — Runic Staff), and a comparison shows that one at least is the origi 
Dal NC- GN. (NB. GND). («oe NB. Calendars 18-11, 12.) 

15 



OE. 

OE.=OLYMPIC ERA. 



Pkeface. 



Petavius calls the first Olympiad : " The torch-light of ancient history." And 
Jarvis says : " From the first Olympiad of Iphitus only, does profane history 
derive its definite form, and detach itself entirely from traditional conjecture." 
Hence the importance of rules to give dates precisely, as counted by the ancient 
Greeks, for the use of historians and astronomers. (NE. Notes 19-36.) 

Such rules have not been found elsewhere. But many detached statements by 
ancient authors furnish sufficient data for the present rules, to give dates precisely 
as counted by the Greeks, during the Metonic and Calippic periods, as proved by 
the numerous examples of eclipses and of new and full moon. 

The first Metonic Cycle was almost precisely astronomic. The Iphitan rules 
transfer this cycle backwards over the previous period. We know that Iphitan 
dates were not thus found. But we know that such was the intention, and that 
the cycles were frequently changed to produce these results, as subsequently the 
Metonic was changed to the Calippic when the Metonic erred one day. Hence the 
inference that the Iphitan rules give dates precisely as counted by the Greeks on 
the introduction of each new cycle, and that the dates were never allowed to vary 
much from what were desired. 

Also, in early times the Greeks had a system of dates counting backwards from 
conjunction. Hence the inference, that at that time dates were strictly astronomic, 
as we know was the case with ancient Hebrews, and with many Mohammedans, up 
to the present time. If this inference be correct, then the Iphitan rules give dates 
precisely as counted by the Greeks at that time. 

Explanatory Notes. 

Olympic Era. (1, 28, 35-38, 65.) 

Iphitan Era. (2, 23-28, 35-37, 47-54, 65.) 

Metonic Era. (3, 5-16, 21, 25, 26, 29, 30, 35, 41-45, 49, 60-62.) 

Calippic Era. (4, 22, 25, 26, 30-34, 40, 46, 61, 62, 65.) 

Metonic Table. (5-16, 20-26, 29, 30, 35, 36, 41-45, 59, 60.) 

Astronomic Accuracy. (9-14, 30-32, 42, 55-57.) 

Historic Data. (2, 15, 16, 29, 32, 47-54, 62.) 

Rules Explained. (17-25.) 

OE. dates are in terms of DJP. (21, 45.) 

First year of Meton's Cycle called GN. 7. (21, 36, 59, 60.) 

Calippic dates average the same in OS. for all time. (22, 46, 65, 66.) 

Iphitan Corrections to Metonic dates. (23, 24, 35-37, 47-54, 65, 66.) 

Examples prove the rules to be correct. (37-40.) 

Contradictions by 

Scaliger, De Emendatione Temporum (41-47). Dodwell, De Veteribus Graecorum, 
Romanorumque Cyclis (48-57). Petavius' Uranologion, in which he translates 
the Greek of Geminus into Latin (58). Jarvis* Chronological History of the 
Church (58). Numbering the years in the cycle (59, 60). Rees' Cyclopedia (61 
62). Long's Astronomv (63. 64). American Nautical Almanac (65, 66). 

1 



OE. 



! 


P 

4-1 





I 

C8 

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a 



T 

s 



II 
z 

H 

M 
- 

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II 

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69 


709 

1802 

2895 
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Table of New 
Moons at Metonic 

New Year in 

terms of JP. Cal. 

at Athens. 




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OE. 



OE. Rule 1. Greek days of the month. 

1. Neomenia, or Nouinenia=New moon. 

1. Prote Archomenou, or Prote Istamenou. 

2. Deutere " " 



3. Trite 


tt 


te 


4. Tetarte 


tt 


5. Peinpte " 


tt 


6. Hekte 


tt 


7. Hebdome " 


it 


8. Oktoe 


ft 


9. Enneate 


« 


10. Dekate 


tt 


11. Prote Epideka, or Prote Mesountos. 


12. Deutere " 


a 


13. Trite 


tt 


14. Tetarte 


" 


15. Pempte " 


ti 


15. =Dichomenia= Middle raoon=rFull moon 


16. Hekte Epideka, or Hekte Mesountos. 


17. Hebdome " 


n 


18. OktoS 


tt 


19. Enneate 


tt 


20. Eikas= Twentieth. 




21. Prote Epeikadi, or Phthinontos Dekate. 


22. Deutere " 




' Enneate. 


23. Trite 




Oktoe. 


24. Tetarte 




' Hebdome. 


25. Pempte 




Hekte. 


26. Hekte 




' Pempte. 


27. Hebdome ' 




Tetarte. 


28. Oktoe 




Trite. 


29. Enneate 


' Deutere. 


30. Triakas=Th 


irtieth ' 


Prote. 



OE. Ride 2. For Olympic lunar dates add 0.400 to standard date found by 
MDB. But for solar dates add 0.036,293 for the longitude of Athens. 



JP. into Metonic. 

OE. Rule 3. "Reduce the given date to DJP., from which subtract 1,431,970, 
and divide R by 6940 for R=GNT>., from which subtract the GND. in the Me- 
tonic Table for R=day of the month which is above, in the year GK which is 
opposite to that GND. Then divide the given year JP. by the circle 19 for R= 
GN. JP. And if this be the same as GN. found, subtract 3933 from the given 
year JP., but if not the same, subtract 3934, and divide R by the circle 4, for Q=*. 
Olympiads and R=the odd year. 

3 



OE. 



JP. into Calippic. 

OE. Rule 4. Subtract 4282 from the given year JP. and divide E by 76 for Q 
(neglecting fractions) = Calippic correction on and after JP. 4384 June 29. Then 
add this correction to DJP. and proceed by OE. Rule 3. 



JP. into Iphitan. 

OE. Rule 5. Subtract the given year JP. from 4301 and divide R by 19 for Q 
(neglecting fractions), which multiply by 0.311,585 for P (including fractions)= 
Iphitan correction, which subtract from the given date for the whole number of 
the day, while retaining the original fraction. Then substitute this corrected DJP. 
for the DJP. of Rule 3, and proceed by OE. Rule 3. 

Except in GN. OE. 14 before JP. 4207, count the month one less than found 
by rule. 

Metonio into JP. 

OE. Rule 6. Multiply the Olympiad by 4, and to P add the odd year, and divide 
S by the circle 19, for Q of cycles+R=GN. Then opposite to that GN. in the 
Metonic Table, and under the name or number of the given month find the GND. , 
to which add the given day of the given month, and the constant 1,431,970, and 
the product of Q multiplied by 6940, and S=DJP. 

But to find the year OE. subtract one from the Olympiad, and multiply R by 4 
and to P add the odd year. 

Calippic into JP. 

OE. Rule 7. Find the Metonic date by Rule 6, and then subtract the Calippic 
correction as found by Rule 4. 

Iphitan into JP. 

OE. Rule 8. Find the Metonic date by Rule 6, and then add the Iphitan correc 
tion as found by Rule 5. 

Except in GN. OE. 14 before JP. 4027, take the GND. in the Metonic Table for 
one month later than the given month. 

OE. EXAMPLES. 
Iphitan Era began JP. 3938 July 9. 



►-5 

3 














o 
O 

-5.9 
-5.G 


O 
& 

5 
14 

2 


New Moon.. . 
New Moon . . . 
Eclipse Lunar 


1 
JP. 3938 July 9.302 
JP. 3947 July 29.723 1 
JP. 3993 Mar. 19.745 


OE. 1 

3 

14 


3 


m. 1 
1 
9 


d. 1.302 

1.728 

15.745 



OE. 



Metonic Era began JP. 4282 July 15. 



New Moon . . . 
Eclipse Solar . 
New Moon. . . 
Ejlipse Lunar 
Eclipse Lunar 
Eclipse Lunar 
Eclipse Lunar 
Eclipse Lunar 
New Moon . . . 



JP. 
JP. 
JP. 
JP. 
JP. 
JP. 
JP. 
JP. 
JP. 



4282 July 

4283 Aug. 
4299 July 
4301 Aug. 
4308 Apr. 

4331 Dec. 

4332 June 
4332 Dec. 
4384 June 



15.958 
3.856 
8.382 
28.942 
16.450 
23.913 
19.097 
13.280 
29.031 













H 












o 










S 


fc 










O 


o 


OE. 87 


y. l 


m. 1 


d. 1.958 





7 


87 


2 


2 


1.856 





8 


91 


2 


1 


1.382 





5 


91 


4 


2 


15.942 





7 


93 


2 


10 


15.450 





13 


99 


2 


6 


15.913 





18 


99 


2 


12 


15.097 





18 


99 


3 


6 


15.280 





19 


112 


2 


12 


29.031 





13 



Calippic Era began JP. 4384 June 29. 



















O 


fc 














g 


ti 


14 














o 


o 


New Moon... 


JP. 4384 June 29.031 


OE. 112 


y. 3 


m. 1 


d. 1.031 


+1 


14 


10 


Eclipse Lunar 


JP. 4513 Sept. 23.677 


144 


4 


3 


15.677 


+ 3 


10 


11 


Eclipse LunarJP. 4514 Mar. 19.801 


144 


4 


9 


15.861 


+ 3 


10 


11 


Eclipse LunarJP. 4514 Sept. 13.044 


145 


1 


3 


15.044 


+3 


11 


18 


Eclipse Lunar! JP. 4540 May 1.241 


151 


2 


10 


15.241 


+3 


17 


12 


Eclipse Solar. 


JP. 4610 July 19.557 


168 


4 


13 


29.557 


+4 


11 



Modern. 



New Year 
New Year 
New Year 
New Year 



AD. 1886 July 27 OS. 
AD. 1905 July 27 OS, 
AD. 1924 July 28 OS, 
AD. 1943 July 27 OS, 

























H 












O 










FJ 


fc 










o 


o 


OE. 666 


y. 2 


m.l 


d. 1 


+30 


6 


671 


1 


1 


1 


+30 


6 


675 


4 


1 


1 


+30 


6 


680 


3 


1 


1 


+31 


6 



OE. NOTES. 



(1). OE.= Olympic era; and Olympic dates in general, and the Olympic year 
counted from JP. 3938 ; and the Olympiad when the odd year is given. Thus in 
OE. dates, JP. 3938=OE. year l = OE. 1. .y. 1. (28, 35-38, 65.) 

(2). The Iphitan era began GN. 5 at the date of new moon JP. 3938 July 9.302 
=OE. l..y. l..m. l..d. 1.302, as shown in the first example. Jarvis (p. 37) 
quotes Censorinus, who says, that the year in which he wrote, was the 1014th 
year from the first Olympiad of Iphitus, and JE. 283 (= JP. 4951), and AE. 267 
(=JP. 4951). Then 1014 from 4951=3937 difference, so that OE. began JP. 3938. 
Then July 9.302 is the date of new moon, next after the summer solstice in JP. 
3938. The examples prove that JP. 3938=OE. l..y. 1. (23-26, 35-37,47-54, 
65.) 

(3). The Metonic era began GN. 7 JP. 4282 July 15.957,890, as in the example, 
at new moon next after the summer solstice. (5-16, 21, 25, 26, 29, 30, 35, 41-45, 
49, 60-62.) 

(4). The Calippic era began GN. 14 at new moon next after the summer solstice 
of JP. 4384 June 29.030, as shown in the example, because the first Calippic correc- 
tion was in JP. 4384. (Long, Vol. 2, p. 675 ; and Rees, Calippic ; Scaliger, p. 13.) 
(22, 25, 26, 30-34, 40, 46, 56, 61, 62, 65, 66.) 

Metonic Table Construction. 

(5). Begin with zero, and continue to add 30 days for the beginnings of the suc- 
cessive months, except when the sum equals or exceeds a multiple of 63 days, sub- 
tract one day and continue to add 30 days to the remainder. (5-16, 20^26, 29, 30, 
35, 36, 40-45.) 

(6). Then set down the distances thus found for the successive 12 months in a 
common year and 13 months in an embolismic year, found thus. 

(7). In JP. 4282 the summer solstice at Athens fell June 27.336,917, and the new 
moon next thereafter fell July 15.957,890. From these data find the date of each 
new moon next after the summer solstice, as for MDT. Table, which reduce to 
calendar time, as in the above Table of New Moons, from JP. 4282 to JP. 4301. 
(MDC. 4th Example.) (59.) 

(8). Then divide each of these years JP. hj the circle 19 for R=GN., which 
begins after midsummer. Then mark as embolismic each year in which the date 
of new moon is earlier than the date in the next year. (HC. Note 59.) 

6 



OE. NOTES. 

Astronomic Accuracy. 

(9). Subtract July 15 (represented by zero in the Metonic Table) from July 
15.957,890, leaving 0.957,890 (the astronomic distance of new moon after the begin- 
ning of the Metonic Cycle). Then continue to add 854.367,068 days for 12 luna- 
tions in a common year, and 383.897,657 days for 13 lunations in an embolismic 
year, to find the equivalents of the dates in the Table of New Moons. 

(10). The whole numbers of the sums are the same as in the first column of the 
Metonic Table, and the fractions are the same as in the Table of New Moons, 
with the single exception of JP. 4286, when the astronomic date is July 1.957, and 
the Metonic date (represented by 1448) is July 2, or 62 minutes later. 

(11). Then, to the astronomic distance in this year (JP. 4286 =GN. 11) =1847.- 
956,751, continue to add lunations of 29.530,589 days until the sum =1831. 854, 41 8 
at the beginning of the next year (JP. 4287), and without exception, the whole 
numbers are the same as in the Metonic Table. 

(12). Hence, while using nothing less than whole days, the Metonic Table makes 
the first days of all these months fall precisely on the days of mean new moon, 
with the single exception of new year in JP. 4286, when the difference is only 62 
minutes. (5-14, 42, 55-57.) 

(13). But this astronomic accuracy for the first 20 years will not remain the 
same during subsequent cycles. Because the Metonic Cycle contained 6940 days, 
while 235 lunations contain 6939.688,415 days. Hence in Metonic time, lunar 
dates recede 0.311,585 days per cycle. To correct this error Calippus omitted the 
last day of each fourth Metonic Cycle (beginning JP. 4384 June 29). This made 
76 Calippic years the same as 76 Julian years. And in Julian time lunar dates 
recede 0.061,585 day per cycle. And the dates in the table can be used for all 
subsequent time to give the mean standard lunar dates. Thus : (MDT.) (14, 40, 
55, 56.) 

(14). From the given year JP. subtract the table year with the same GN.. and 
divide R by 19 for Q of cyles, which multiply by 0.061,585 for the recession, which 
subtract from the table date for the approximate date. Then subtract JCC. for 
the table year, and add JCC. for the given year, and subtract 0.400 that Meton's 
dates exceed standard, and the result will be the same as found by MD. Thus the 
present year AD. 1886=GN. 6 is 121 cycles after JP. 4300=GN. 6, with new moon 
July 27.279 Metonic. Then 121x0.061,585= -7.452 recession leaves July 19.827 
approximate, -0.75 JCC. for JP. 4300,+0.50 JCC. for AD. 1886,-0.400 for 
Meton's standard=July 19.177 Cal. Stand. OS., as found by MD. Add 12 NS. 
SC.=July 31.177 mean NS., while the actual in the Nautical Almanac=July 
31.226. (MD. Second.) 

Historic Data (2, 15, 16, 29, 32, 47-54, 62). 

(15). Meton and Euctemon determined the date of the summer solstice at Athens 
in terms of the Era of Nabonassar= JP. 4282 June 27 at 5 or 6 hours after mid- 
night. (NE. 2d Ex. ; MD. 4th Ex.) They do not give the date of new moon. But 
Table I. shows that it was accounted about 0.400 more than standard time by 
MDB. (20.) Dodwell (Jarvis, p. 21) says : " As far as we know, the inhabitants 
of Elis never reckoned the beginning of their cycles from any other point than the 
summer solstice. . . It is highly probably, that the Olympiads had been celebrated 

7 



OE. NOTES. 

from the 11th to the 16th of the lunar month after the summer solstice." Jarvis 
(p. 20) quotes Plato (about JP. 4350), who says : " When the new year is about to 
commence after the summer solstice at the coming in of the month." Scaliger (p. 
36) says : " The oracle was interpreted to signify, that the Olympiad must be cele- 
brated at the full of the moon, which fell precisely on the 15th of the first month." 
Pindar (Jarvis, p. 18) shows : "That the Olympic Games were celebrated from 
the 11th to the 16th of the first month, or in other words, for five days, preceding 
and including the dichomenia or full moon." One Scholiast (Jarvis, p. 18) says : 
" The Olympic contest takes place at the full moon, and the decision of the judge 
is pronounced on the 16th day of the month." Another says : " The contest takes 
place at one time after 49 months, at another after 50 months." Geminus (Jarvis, 
pp. 12, 16) says : "To measure the days according to the moon, consists in making 
the denomination of the days follow the illumination of the moon." And see the 
remarks by Thucydides and by Geminus. (29, 32, 47.) (Petavius, pp. 32, 33.) 

(16). Geminus describes the Metonic Cycle, as quoted by Petavius in his Urano- 
logion, and in English, by Jarvis (pp. 17, 18), in substance thus: " The Metonic 
Cycle had 19 years (of which 7 were embolismic)=6940 days =235 months, of 
which 125 were full (30 days) and 110 were hollow (29 days). Then 6940-^110= 
63 ratio. So that counting each month 30 days, one day was retrenched after 
the sum of days thus found exceeded a multiple of 63 from the beginning. And 
this sometimes brings two months of 30 days together." (5-8, 15, 41-46.) 

OE. Rules Explained. 

(17). OE. Rule 1. The days of the months were divided into three decades, and 
counted as 1st, 2d, etc., of each decade. The first decade was called Archomenou 
(of the beginning), or Istaminou (of the present). The second was Epideka (after 
the tenth), or Mesountos (of the middle). The third was Epeikadi (after the 
twentieth). 

(18). Also, the first day was called JSTeomenia, or Noumenia (new moon), the 
15th Dichomenia (half month), the last Triacas (30th), even when the month had 
only 29 days ; also Enekainea (the old and the new), also Demetrias. 

(19). Also, the last decade was counted backward from the first day of the next 
month, and the 21st was called Dekate Phthinontos (the tenth before the Lost 
moon) if the month had 30 days, or one less if the month had 29. And Long 
(Vol. 2, pp. 517, 518) quotes a passage from Homer which contains the words 
Phthinontos and Istaminoio, and from " Solon who reformed the Greek months." 
But he translates Phthinontos as "waning." (63, 64.) 

(20). OE. Rule 2. The lunar dates in the table of examples are 0.400 more than 
standard dates found by MDB. or MDT. Because Table I. shows that this was 
the Metonic standard, and perhaps gives the actual date of new moon at Athens in 
JP. 4282. (MD. Second.) For the longitude of Athens add 0.066,296 to stand- 
ard time (Local). (27-40.) 

(21). OE. Rule 3. The construction of the Metonic Table shows that Meton 
counted each day as one day advance in date, while our Julian dates make 
no account of the extra day in a bissextile. Hence these rules are in terms of 
DJP. Then the Metonic Cycle began JP. 4282 July 15=DJP. 1,563,831. This 
being date, subtract one day to bring it to distance corresponding with GND. in 

8 



OR NOTES. 

the Metonic Table. Then OE. began JP. 3938=19 cycles =131, 860 days before 
the Metonic Cycle, and this from 1,563,830 leaves the constant 1,431,970. Then 
JP. 3938-^19 leaves GN. JP. 5, which begins Jan. 1. Then to simplify the calcu- 
lation, JP. 3938 =GN. OE. 5, which begins after the summer solstice of GN. J P. ■ 
5, and ends in JP. 3939=GN. JP. 6. Hence JP. 3938-8933=5;-h4=OE. 1. .y. 1 
after the solstice in JP. 3938, but JP. 8989-3934=5;-r-4=OE. 1. .y. 1, before the 
solstice in GN. JP. 6. (5-8, 35, 86, 59, 60.) 

(22). OE. Rule 4. Calippus made no change in the Metonic Cycle, except at the 
end of each fourth Metonic Cycle (counted from JP. 4282) he counted the last 
Metonic day the first day of the Calippic year, but made the first correction in JP. 
4384, by counting June 29 as OE. 112.. y. 8..m. l.d. 1. Hence the Calippic 
Cycle =27, 759 days =76 Julian years, and hence on an average, the dates in the 
Metonic Table will for all time remain the dates OS. for the same GN., to which 
NS. SC. must be added for dates NS. But there will at times be the difference 
of one day, and the precise date must be found by Rule 4, since Calippic dates do 
not run parallel with Julian dates, while the average is the same. (21, 88, 34, 40, 
45, 46, 65, 66.) 

(23). OE. Rule 5. The Iphitan correction of 0.311,585 day per cycle, is the dif- 
ference between 6940 days in the Metonic Cycle and 6939.688,415 days in 235 mean 
lunations of 29.530,589 days. Then the year JP. from 4301 and Rh-19 for Q 
(neglecting fractions), gives the number of cycles that the year JP. is before the 
year with the same GN. in the standard Metonic Cycle. Then Qx 0.311, 585 from 
the given date, gives the fraction belonging to the standard Metonic date, while 
the original fraction belongs to the original date. (2, 23-26, 35-37, 47-54, 65.) 

(24). The Metonic new moon of GN. 14 fell 1.192,388 day after the summer 
solstice in JP. 4289. Its advance of 0.004,542,68 day per year in solar date makes 
it coincide with the summer solstice in JP. 4027. Before that date it fell before 
the summer solstice. This correction makes Iphitan dates bear the same relation 
to the summer solstice as the Metonic dates during the first Metonic Cycle. 

(25). Neither Meton nor Calippus had analogous rules for subsequent dates, 
(MDT. Mosaic Explanation.) (28, 38, 39, 47-54.) 

(26). OE. Rules 6, 7, 8, are the reverses of OE. Rules 3, 4, 5. And the sum of 
years first found is 4 years more than the year OE., to simplify the rules. Thus 
OE. year l = OE. 1. .year 1. Then by rule 6 ; OE. Ix4;+1=5;--19=Q0.4-GN. 5 
== 5 ; ^_4-OE. 1. .y. 1. Hence JP. 3938 = OE. 1. .y. 1 is called GN 5. And this 
accidentally makes OE. GN. and JP. GN. the same at the beginning of the year 
OE. (21, 26, 35, 36, 59, 60.) 

OE. Examples. 

(27). The dates of eclipses and of new and full moon are found in standard 
time by MDB., with the addition of 0.400 to correspond with Meton's dates. The 
actual dates may have been a few hours different. (20,) 

(2§). The Iphitan examples, show that the rules for Iphitan dates, make new 
moon fall on the first, and full moon fall on the 15th day of. the Olympic month. 
The year JP. 3947 is one of the excepted years (GN. 14) in OE. Rule 5. The 
eclipse of JP. 3993 is the earliest astronomic date on record. (NE. Note 3 ; MD. 
2d Ex.) (2, 23-28, 85-37, 47-54.) 

(29). The Metonic examples show that from the beginning of the Metonic 

9 



OR NOTES. 

Cycle Until JP. 3984, new moon fell on the 1st, and full moon on the 15th of the 
Metonic month. And with respect to the eclipse of JP. 4283, Thucydides says 
that it occurred " at the noumenia according to the moon, when also only docs it 
appear possible 1o happen." (Scaliger, p. 81 ; Jarvis, p. 4.) t3, 5-10, 21, 25, 20, 
29, 30, 35, 41-45, G0-02.) 

(30'. The example of JP. 4384, shows that the recession of 0,311,585 day per 
cycle, caused new moon to fall on the last day of the Metonic year, when Calippus 
added one day to the date and made it the first day of the next year. (4, 22, 25, 
23, 30-34, 40, 48, 5G, 01, 02, 05, 06.) 

(31). The Calippic examples show that the Calippic corrections (of 1 day in 
JP. 4384 and 3 in 4513, 4514, 4540), were sufficient to make the dates fall as in the 
first Metonic Cycle. But the Calippic correction of 4 days in JP. 4010, was not 
sufficient to correct the Metonic recession of 5.297 day, so that in JP. 4010, the 
solar eclipse fell on the Triacas. (32.) 

(32). This will explain the "fixed law" mentioned b} r Geminus, who wrote JP. 
4037, and says ; " The solar eclipses always fall on the Triacas, for then the moon 
is in conjunction with the sun. And according to some fixed law it is that the 
eclipses of the moon take place in the night which precedes the Dichomenia, for 
then the moon is diametrically opposite to the sun." (Jarvis, p. 13.) (4, 13, 15, 
81, 32.) 

(33). The last four examples of GN. 0, are in four successive Metonic Cycles, 
and the first three in one Calippic Cycle with 30 days correction, and the last 
in the nest Calippic Cycle with 31 days correction, and three in common years 
while AD. 1924 is a leap year. And three of these new years fall on July 27, OS., 
which is the same as GN. in the Metonic Table, while the fourth falls on July 
28 OS. This shows, that while 70 Calippic years contain the same number of 
days as 70 Julian years, the dates OS. are not always the same as in the Metonic 
Table. (4, 22, 46, 05, 08.) 

(34). In like manner, the Calippic new year in JP. 4384= GN. 14 falls June 29, 
while the Metonic new year in JP. 4289=GN. 14 fell June 28. (22, 40.) 

Details of Calculation. 

(35). Example 1st. JP. 3938 July 9.302=OE. l..y. l..m. l..d. 1.302. Then 
by MDB. find the standard date of new moon, and by OE. Rule 2 add 0.400= JP. 
3938 July 9.301, 095=DJP. 1,438,178.301,095. Then by OE. Rule 3 subtract the 
constant 1,431,970=0209.301, 695;-=-G94O=Q0.+GND. 0209.301,695 which is next 
more than 0202 of GN. 5 month 1, in the Metonic Table, which subtracted, leaves 
month 1 day 7.301,095 Metonic. Then JP. 3938^-19 = GN. 5. This being the 
same as found by rule, subtract 3933 from JP. 3938=5;^4=OE. 1. .y. 1 with m. 
l.d. 7.301,095 Metonic. 

(38). These are standard rules for all cases, and OE. 1. .y. 1 is countod GN. 5, 
to simplify the rules, so that 5-h4=OE. 1. .y. 1. (21, 30, 59, 00.) 

(37;. Then (by OE. Rule 5) 4301-JP. 3938=368; -f-19=Q 19;X0.311,585= 
5.920,115, which from d. 7.301,095 leaves d. 1.381,580, for the whole number, 
day 1, with the original fraction day 1.392. Because the original, fraction is the 
actual date while the fraction as found is the original date reduced to the date of 
the corresponding GN. in the Metonic Cycle, at JP. 4299 July 8.382.. And. in this 

10 



OR STOTES. 

case the Metonic date is first found, to illustrate the standard rule, and then 
the Iphitan correction is subtracted. This is the same in effect as subtracting- 
the correction 5.920,115 from DJP. 1,408,178.301,695 and then proceeding as 
before. (20.) 

(3§). Example 2d. For the exceptions in OE. Rule 5. Then JP. 3947= GN. 14. 
And JP. 3947 July 29. 727, 663= DJP. 1,441,486.727,663= OE, 3. .y. 2. .m. 2. .d. 0.- 
727,663 Metonic. Subtract the Iphitan correction 5 608,530, and retain the orig- 
inal fraction, leaves month 2. .d. 1.727,663. But this being GN. 14 before JP. 
4207, count it one month less=OE. 3. . y. 2 . . m. 1 . . d. 1.728. (24.) 

(39). In the Metonic Table new year of GN. 14 (JP. 4289) falls June 28 and 
after the summer solstice. But in JP. 3947 the same moon falls 0.553 day before 
the solstice, and the next moon fell July 29,727,633, (7, 24.) 

(40). Example 13th. Calippic New moon JP. 4384 June 29.031 = OE. 112. .y. 3 . 
m. 12. .d, 29,031 in OE, GN, 13 Metonic. (But JP. 4384-r-19=JP. GN. 14.) Then 
OE, GN. 13 will show all the details of that year in the Metonic Table. And GN. IS 
is a common year of 12 months, and the last month had only 29 days (2511 to 2540 
days after the beginning of the cycle). Hence OE. 112. .y. 2 m. 12 d. 29.031 
was the last Metonic day in that year. At this point, Calippus made his first cor- 
rection by advancing the date one day, and this made the same absolute day JP, 
4384 June 29, to be OE, 112. .y. 3. .m. 1. .d. 1.031, and the Calippic new year of 
OE. GN. 14, and the same as JP. GN. 14. (4, 21, 22, 62.) 

Contradictions. 

(41). Contra. First. Scaliger (p. 78) gives his theory, and says : " Geminus, an 
ancient and erudite author, signally fails, who writes that Meton divided 6940 by 
110 syzygies, and because 110 is contained 63 times in 6940, therefore he thinks 
that Meton immediately after 63 days, made the retrenchment of days. The ratio 
itself refutes this/' (57.) 

(42). Now : Geminus of Rhodes was a Greek astronomer and mathematician, 
who wrote (about B.C. 77) his account of the cycle which he himself used, as shown 
by his remark, that solar eclipses always fell on the Triacas, etc. And such 
authority for a contemporary fact, is more reliable than Scaliger's theoretical 
assertion (in a.d. 1629; that he " signally fails." Ou the contrary, the Metonic 
Table shows that Scaliger is in error, since that table is constructed precisely as 
directed by Geminus, and the "ratio of 63" produces precisely the results stated 
by him. And its astronomic accuracy is very remarkable. (5-16, 29, 32, 49, 58.) 

(43). Contra. Second. Scaliger (p. 80) gives his " Table of Metonic Neomenia in 
Julian months," and puts 6 of the 7 embolismic months in December, and one on 
January 1. 

(44). Now : December is the last Julian month. But the embolismic months 
were necessarily the last months of the Metonic year, and necessarily included the 
date of the summer solstice, which at that time fell on June 27, as determined by 
MDB. and by Meton. (MD. 4th Ex.) (7, 59.) 

(45). Contra. Third. Scaliger (p. 80), in his table, does not give the years JP. 
But (p. 13) he shows that it began J P. 4282. And his days of the month prove it, 
since the years begin at the same dates as in the Metonic Table, except one day 
later an JP. 4291 and JP. 4298. Hence, on these days, he differs from the state 

11 



OE. NOTES. 

merits by Geminus. The other dates have not been compared. And this is " A 
Table of Metonic Neomenia in Julian months," which make no difference for 
the extra day in a bissextile, while Meton counted every day as one day advance 
in date. (5, 16, 21, 33, 34.) 

(46). Contra. Fourth. Scaliger (pp. 89, 90) gives his version of " The Table of 
Neomenia of the Calippic Period." This is for 76 years, and is not a repetition of 
his version of the Metonic Cycle. But Calippus made no change in the Metonic 
Cycle, except at the end of 76 years, he counted the last day of the Metonic year, 
the first day of the Calippic year, as in the example JP. 4384 June 29. (4, 22, 
30, 40.) 

(4 1 ?"). Contra. Fifth. Scaliger (p. 24) says that Thucydides says, that the solar 
eclipse of JP. 4283, happened at "Noumenia according to the moon. Therefore 
there was a certain noumenia not according to the moon. Diodorus Siculus in Book 
12, writes that Meton, the astronomer, established his cycle on the 13th Skirropho- 
rion, so that it is manifest that the new moon of that Skirrophorion was not lunar." 
This contradicts the Iphitan rule. But the conclusion is not justified by the prem- 
ises, since this eclipse of JP. 4283 was in the second year of the Metonic Cycle, 
when the examples prove, that this was not only "a certain noumenia according 
to the moon," but that this was the general rule. (3, 9-12, 14, 29.) 

(4§). Contra. Sixth. Dodwell says that Diodorus Siculus asserts, that the Me- 
tonic Cycle began on the 13th Skirrophorion. And Jarvis (p. 19) says, "from this, 
Dodwell infers, and it seems justly, that in consequence of defective cycles previ- 
ously in use, an error of 17 or 18 days had occurred, which was then rectified by 
leaving out the remainder of Skirrophorion, and on the 13th of that month com- 
mencing the first month Hekatombaion after the summer solstice." 

(49). Now, Scaliger and Dodwell contradict the historic data upon which the 
Iphitan rules are founded upon the single statement of Diodorus, who wrote about 
400 years after the eclipse of JP. 4283 to which Scaliger refers, and therefore does 
not state a contemporary date, as does Geminus, which Scaliger denies. And 
Lemprierre, in his Classical Dictionary, says of Diodorus : " His manner of reckon- 
ing by Olympiads and the Roman consuls will be found very erroneous." (2, 
15, 42.) 

(50). Dodwell' s inference supposes, that the philosophic Greeks, who "named 
the days according to the illuminations of the moon," called the day of new moon 
Dichomenia, and the day of full moon Neomenia, and held the Olympic Games on 
the 15th of the month, during the Lost moon, while we know that they frequently 
changed their cycles, to make the names of the days correspond with the illumina- 
tions of the moon. (15, 29, 32.) 

(51). But, supposing in this case, the statement by Diodorus to be correct, it 
can be interpreted in two ways, to agree with all the historic data upon which the 
Iphitan rule is founded, (15.) 

(52). First. Mean full moon fell at Athens JP. 4282 June 30.793, which by the 
Iphitan rule was Skirrophorion 15.793. And as the Romans had a Proleptic Julian 
year, to correct dates, before the standard date of the Julian Calendar, at new 
moon, dated Jan. 1 BC. 45, so the Metonic date may have been established at full 
moon, now called the 15th, but previously the 13th, to correct an error of two 
days, and not 17 or 18 as Dodwell supposes. (JE. Note 2.) 

(53). Second, In the analysis of the first Roman Calendar, it is supposed (con 

12 



OE. NOTES. 

trary to authority) that Romulus adopted the calendar of a Greek colony, and that 
the months began at the astronomic date of new moon, as we know was the fact 
in the early Hebrew Calendar, and is now the fact with many Mohammedans. 
And that the word Ides is not "derived from the obsolete iduare to divide, because 
it divides the month," but from the Greek word Eido (pronounced Ido), to see or 
take an observation on the hour of full moon, and thence determine the number of 
days to the next new moon, called Kalends by the Romans from the Greek word 
Kaleo, to call out or make proclamation of the uumber of days to the next new 
moon. And this Proclamation (Kaleo) made day by day, caused the Roman dates 
to count backwards. In like manner, OE. Rule 1 shows that in early times the 
Greeks had a system of dates counting backwards, and the remark by Diodorus 
might indicate, that at full moon JP. 4282 June 30, a Proclamation was made, 
that 15 days thereafter would be new moon, and the Metonic Cycle would 
begin. (AU.) 

(54). Either of these suppositions makes the error two days, and reconciles the 
apparent contradiction by Diodorus to all the historic data upon which the Iphitan 
rule is founded. (2.) 

(5*5). Contra. Seventh. Jarvis (p. 21) quotes with apparent approval the remark 
by Dodwell : "To date exactby the beginning of each year according to our com- 
putation, would oblige us in every instance to calculate the lunations. This would 
be unnecessary trouble. It will be sufficient to take the first day of July as the 
beginning of an Olympiad, and thus reckon the first six months as belonging to 
one, and the last six months as belonging to another of the four years consisting of 
49 or 50 lunar months into which the Olympiads were divided." 

(56). Now, a calculation of lunations would not give the date "exactly," since 
neither the Metonic nor the Calippic Cycle was "exactly" astronomic for distant 
dates. And some months had 30 and others 29 days. (13, 16, 24, 31.) 

(57). Also, the Metonic Table shows that in the first cycle, the beginnings of 
the years varied from June 28 to July 27. So that it is not obvious, what use an 
astronomer or a historian could make of this rule, while Scaliger's rules were 
printed AD. 1629, and although not precisely correct give close approximations. 
(5-7, 41-46.) 

(58). Contra. Eighth. Petavius, in his Uranologion (in which he translates the 
Greek of Geminus into Latin), says that the Calippic Cycle contained 22,759 days. 
This is a misprint for 27,759 days. Also Jarvis (p. 18) has the same error. (4, 22, 
46, 01.) 

(59). Contra. Ninth. Long (Vol. 2. p. 515) states that the embolismic months 
were inserted at the ends of the years 2, 5, 8, 10, 13, 16, 18 of the cycle. But he 
does not state the absolute years. Also Scaliger (pp. 78-92) marks the same years 
as embolismic, when the first year of the cycle is counted GN. 1. But he does not 
give the absolute years. Geminus only says that there were 7 embolismic years, 
without stating the number. (6, 7, 16.) 

(60). Now, the Metonic Table shows that the years of the cycle GN. 8, 11, 14, 
16, 19, 3, 5, are embolismic as used herein. All cycles of 19 years necessarily have 
7 embolismic years, and those necessarily fall in certain absolute years, as in the 
Metonic Table. But the numbering of the year in the cycle (or its GN.) is arbi- 
trary, and the dates of new year in Scaliger's Table (p. 80) prove that he counts 
JP. 4282 as GN. 1. This was probably Meton's arrangement. But JP. 4282 is 

13 



OE. NOTES. 

herein counted GN. 7, so that JP. 3938 shall be GN. 5, to simplify the rules. The 
difference is in form— not in substance. (8, 21, 26, 36.) 

(61). Contra. Tenth. Scaliger(p. 13) says that Meton counted 6940 " solid days," 
to convert which the Calippic period of 27,759 days without a fraction succeeded 
in the 108d year after the beginning of the Metonic. Also Rees (Calippic) says 
that the Calippic period began JP. 4384=OE. 112.. y. 3. Also Long (Vol. 2, 
p. 695) says that it began at midsummer BC. 830. 

(62\ Now, JP. 4282 to 4384=102 years as we count. But Scaliger habitually 
includes both extremes in the Roman mode and calls it 103. So that all agree that 
the Calippic era began JP. 4384, as in the example. But it began on June 29 JP. 
4884 at new moon next after the summer solstice, and not at the solstice. (7, 30, 
40, 44.) 

(63). Contra. Eleventh. Long (Vol. 2, pp. 517, 518) says : " In this last decade, 
the moon was so much in the wane, that they gave it a name from a word that 
signified to decay or perish, reckoning the days backwards from the last day of the 
month, and calling the 21st day Debate Phthinontos, the tenth of the waning or 
tenth from the disappearing moon if the month consisted of 30 days, or Enneate 
Phthinontos, the ninth of the waning if the month consisted of 29 days." (19.) 

(6 &). Now : In a month of 80 days, the 21st is the 10th day before the beginning 
of the nexth month. Hence these dates count backwards from the invisible new 
moon, since such was the new moon of the Greeks, and not the visible new moon 
of the Hebrews and Mohammedans. And since Phthino signifies to wane or per- 
ish, this must signify that the moon has perished or is Lost. If it signified wan 
ing, the dates should count forward from the 15th and be always the same. (19.) 

(65). Contra. Twelfth. The American Nautical Almanac gives AD. 1886=GN. 
6=OE. 666 y. 2, " commencing in July, if we fix the era of the Olympiads. . . . 
near the beginning of July of the year 8938 of the Julian Period." 

(66). Now, there is only one point in which this differs from the rules herein, 
if counted in NS., since new year fell on July 27 OS. = Aug. 8 NS., as shown in 
the examples. The Greenwich Nautical Almanac does not give Olympic dates. 
(1, 2, 22, 33, 34.) 



14 



OS, 



OS. = Old Style as used by the Westerns before (NS. 18)* 

1. (1). DOMINIC 1L., by memory for all time. 
Subtract one from the year JP. Then 

Add this one and the remainder and its fourth, and dividing by 7. 
What is left take from 7, and the letter is given. 
(2.) Or from the year AD. 

Add 4 and the year and its fourth, and dividing by 7, 
What is left take from 7, and the letter is given. 
And the conditions are the same as (NS. 10-2, 3.) 
(3.) Or by (NS. 9), find the year of the Solar Cycle, then opposite to that year 
find for all time the OS. Dominical in the following table. 



1 


g. F 


5 b. A 


9 d 


C | 13 


f . E 


17 a 


G 21 


c. B 


25 


e. D 


2 


E 


6 G 


10 


B 14 


D 


18 


F 


22 


A 


26 


C 


3 


D 


7 F 


11 


A 15 


C 


19 


E 


23 


G 


27 


B 


4 


C 


8 E 


12 


G 16 


B 


20 


D 


24 


F 


28 


A 



To memorize this table, A 
the Leap Years. 



28, and the others in succession, are doubled at 



2. (1.) EASTER. Find GN. (NS. 15) and OS. Domini- 
cal. Then, in the adjoining table, find the date next after 
the date opposite to GN., which has the Sunday letter same 
as the Dominical, and that is the date of OS. Easter, called 
Hagion Pascha by the Greeks. (AM. 7.) 

(2.) Or by memory. Multiply GN. by 11 ; divide the 
product by 30, subtract the remainder from March 47 (the 
perpetual Key date), and the second remainder is the date 
of full moon (OS. FGND.) if on or between March 21 and 
50. If not, then add or subtract CO days to bring it there. 
Then find the Ferial for that date by (OS. 3), and Sunday 
next thereafter is Easter. (NB. GND. 12.) 

3. (1.) FE RIAL, or day of the week. Find OS. Dom- 
inical, and thence the Ferial dated OS. by (NS. 13). 

(2.) Or divide the year AD. by 4 for quotient and re- 
mainder. Then multiply the quotient by 5, and to the 
product add the remainder, and the constant 1, and the 
day of March, OS. Then divide the sum by the circle 7, 
and the remainder 1 to 7 = Sunday to Saturday. (AM. 7.) 

4. LEAP YEAR. Divide by 4 the year AD. or the 
odd years omitting the centuries, and if there be no remain- 
der the year is OS. Leap Year. 

5. MOVEABLE FEASTS. Find from the date 
of OS. Easter by 'NS. 6.) 

* See NS. Preface, and AC. Notes 81-131: AM. Notes. 



Date. 



March 21 

" 22 

" 23 

" 24 

" 25 

" 26 

" 27 

" 28 

29 

30 

" 31 

April 1 

2 

3 

4 

5 

6 

7 

8 

9 

" 10 

" 11 

" 12 

" 13 

" 14 

" 15 

" 16 

" 17 

18 

" 19 

20 

" 21 

" 22 

" 23 

" 24 

" 25 j 



GN. 



SCALE.* 

The SCALdE to measure dates from any standard GN. and GND. first appears 
in AIT. NGN. (NB. GND.) It can be thus formed : 

1. By Addition. Assume any date as the first limit, and 29 days thereafter as the 
second limit, and any GN. and GND. as the standard, on or between these limits, 
as Jan 80 and 109 for OS. FGN. in (NB. GND.) Then to any GN. add 8 in a cir- 
cle cf 19 ; (£ e.^ add 8 or subtract 11), and if this produce GN. 1 to GN. 8, date it 
one day later, but if GN. 9 to GN. 19, date it two days later ; and if this exceed 
the second limit, then subtract 30 days for the same GN., and continue the addi- 
tion until the original GN. and GND. are reproduced. 

2. By Subtraction. From GND. of any GN. subtract 11 days to find GND. of the 
next GN.; except from GND. of GN. 19 subtract 12 days to find GND. of GN. 1. 
And, in any case, if this bring the date before the first limit, add 30 days for the 
date of the same GN., and continue to subtract as before until the original GN. and 
GND. are reproduced. 

3. For a Double Scale continue the addition (1) until two series of 19 GN. are 
dated. These will fall on or between the limits of 59 days. 

4. For a Full Cycle of 235 moons in 19 years, add continually 59 days to each of 
the dates in the double scale, in a circle of 365 days on or between Tan. 1 and 365, 
until all the original GN. and GND. are reproduced. That is, when the date of any 
ON. exceeds Jan. 365, then subtract 365, and add one to GN. Except, thus find the 
-date of GN. 1 from GN. 19, and then subtract one day from the date of GN. 1, and 
continue as before. Or count the year GN. 19 = 368 days. 

5. By alternation. Take any date as the single limit, and any GN. and GND. less 
than 30 days thereafter as the standard ; as the limit Jan. 67 and AM. NGN. 3 = 
Jan. 82 in (NB. GND.) Then to GND. add 30 and 29 days alternately, markin.o; the 
same GN. at eaeh addition, in a circle of 365 days, and adding one to GN. when 365 are 
subtracted, and thus continue the alternation until GND. passes the limit, and thus 
find GN. 4 = Jan. 71. Then taking GN. 4 = Jan. 71, proeeed as before to find 
GN. 5 = Jan. 90. Thus continue each time to begin the alternation with 30 and 
29 after passing the limit. Except eount the year, GN. 19 = 366 days, and subtract 
that number when GND. of GN. 19 exceeds 366, to find GND. of GN. 1 ; and thus 
continue until the original AM. GN. 3 = Jan. 82 is reproduced. 

6. Omitting some remarkable properties of this scale, which are simply curious, 
since it was found to be not accurate enough for dates in the ancient Olympic cal- 
endar (OE.); the entire cycle thus divides itself into 6 double scales, with 7 embolis- 
mic months. Six nodes are thus formed where the double scales join. This node 
is indicated by GN. 9 to 19 falling on the date next after GN. 1 to 11, thus showing 
that the scale is broken at this point, as at AU. NGN. 9 = April 1, and NC. NGN. 
i6 at April 6, while NGN. of CP. 1553 is full of nodes and extra spaces. 

7. The full eyeles NC. NGN. and AU. NGN. (in NB. GND.) are nearly as de- 
scribed in (5th) but not exaetly. (NB. AC. 3, 28). AM. FGND. are not by scale in 
the present form. But to AM. GN. add 3 in a circle of 19, and AM. FGND. becomes 
OS. FGND. The simplicity of the rules (AC. and NS. 11, 12, 14, 20, 21), arises 
from the peculiarity of the seale. The same rules will not apply to (AM. 3, 4), 
because the transfer of the dates of (OS. FGN. to AM. FGN. in NB. GND.), breaks 
the ?cale or correspondence between GN. and GND. Hence (NB. NS, 3, 11, Ex "> 

* See Preface to NS. The Esryptian rules form a Scale, wh'eh wa< made equidistant with the 
printed lines, when examining the cycles of v inch par?* are given in GND. In the Appendix 
the*e mle.s axe called GN. Rule s. (AC. Notes 53-74.) 



APPENDIX. 






A.=a reference to this Appendix. 

A=Adu=Day i. .iv. .vi (HC), i. e., see HC. 

AC.= Amended Calendar (C), i. e., see AC. among the Calendars in its alphabeti- 
cal order. 

Actual dates are sometimes more and sometimes less than mean dates. And 
mean dates are chosen between the extremes to he as near as possible to actual 
dates. Then other rules are required to find the corrections to the mean so as to 
find the actual. The mean dates of FGN., NGN., VGN. are given under the 
headMD. 

AD. = Anno Domini=Year of our Lord=Dionysian Era=our usual dates (AM., 
BC, HC, JP.), i. e., see those symbols in A. 

AE. =Actian Era of the Egyptians (C), i. e., see AE. among the Calendars. 

Age of the moon = days after conjunction. In general terms it signifies the days 
after the date of any zero (GN., Zero). 

A GND.= Apogee GND., or the date when the moon is furthest from the earth, 
and PGND. = Perigee GND., or the date when the moon is nearest to the earth. 

AJR=JP. 

Alexandrian Canon (AC, NC.) 

J.Jf.=Russo-Greek Calendar (C)=Anno Mundi=Year of the Worlds AD. 4- 
5508. Also Before Noon. And 0.00 to 0.50 stand. =0 to 12 hours counted from 
midnight at Greenwich. And in HC, 6 to 18 hours=AM. But Lindo says if the 
hours are more than 12, they are so many past noon, and he marks them (erro- 
neously) "M" and " A" (HC. Table). 

AM. GJV.=GN*, found from AM. (AM) Chronological. 

ANA. — American Nautical Almanac (GNA., PNA.). 

Anglican= Church of England and its descendants (NS.,. AC). 

Apogee (AGND.). 

AR. = Right Ascension = Angular distance from the first point of Aries measured 
eastward along the Equator, and given in sidereal time (Equinox, Zodiac). 

Astronomic rules (MD.). 

A £7".=AUC=Anno Urbis Conditoe=Year of the City (of Rome) Constructed^ 
Did Roman year (C), before the introduction of the Julian Calendar= JE. (C) 

Authors are named in the notes. (AC 132 ; ME. 25 ; HC; NS. 3.14.) 

#.=Betuthakphat=II. .15. .589= Hebrew numeral (HC). 

B.A.=ihe present author = original. 

Basic=the earliest standard. 

Basic age of zero=age of zero at the beginning of JP. Rule. Reduce the as- 
sumed standard mean date of zero to the year JP. and Jan. Cal. OS. stand., and 
this into DJP. , which divide by a revolution of zero to whole numbers in Q, and 
subtract R from a revolution and 2d R= Basic age of zero. Thus, the standard 
FGND., AD. 1853, Sept. 17.993,023 Cal. ; NS. ; stand, produces the Basic age of 
FGN. =5.078,489, and of NGN. =19.843,783. And the standard VGND., AD. 
1866. March 20.837,442, Cal. NS. Stand, produces the Basic age of VGN.= 
246.701,622. All are in terms of JP., Jan. Cal. ; OS. Stand. (MDB.). 

1 



APPENDIX. 

BC.=Before Christ (AD., JP.). 

Bissextile= JC 0, but differs from a leap year which is also JC. 0. The bissex 
tile has its intercalary, " Bis-sextum Kalendas Martii," or second Feb. 24, as we 
count, while the intercalary in a leap year is Feb. 29, and in astronomical calcula- 
tions, subtract one from the year JP. and divide by 4, and if there be no re- 
mainder, the year is accounted a bissextile or a leap year — invariably. But through 
error, the actual Roman bissextiles did not fall on the regular years from JP. 
4672 to JP. 4718 (JE., AE.). 

Building of Rome (AU.). 

G = Calendars in their alphabetical order (Era). 

Cal.= Calendar or ordinary dates, and in JC. has Feb. 29 and 366 days, and in 
JC. 1, 2, 3 has 365 days. And the days always begin at the same hour, as Stand. 
Call begins at midnight at Greenwich. But Julian time has no Feb. 29, and all 
the years=365.25 days, and Min. Stand, begins the day, after Cal. Stand. =0 hours 
in JC. ; 6 hours in JC. 1 ; 12 hours in JC. 2 ; 18 hours in JC. 3 ; 24 hours in JC. 
4 (Jan. Cal., Month Cal., Jan. Min., Month Min.), JCC. 

Calends or Kalends =Begirmmg of the month (JE. Table). 

Calendars Compared (C, AC. Notes 81, 85, 89 ; HC. Note 157). 

Calippie cycle (OE.). 

Canicular, or Wandering Year (NE., AE.). 

Chalcedonian Calendar=AM. and OS. (AC). 

Characters Measure of time, and a date (HC). 

Circle. Rule. To divide by a circle, make Q one less than by ordinary division 
if the remainder would be nothing, so that the remainder may be the full num- 
ber of the circle. To add in a circle, subtract the circle when the sum is greater 
than the circle. To subtract in a circle, add the circle and then subtract if without 
the circle the remainder would be nothing or negative. 

Civil time counts from midnight at the given Longitude (Standard, Hebrew, 
Local). 

Common year= JC. 1, 2, 3=365 days. Also HC. year of 12 months (Bissextile, 
Leap, Embolismic). 

Concurrence is here used to signify the year, when the full moor, represented by 
any GN. falls at the same date as the vernal equinox (MDT. Mosaic). 

Conj unction= NGN. = moon close to the sun and invisible=new moon of the al 
manacs. 

Constant=a, quantity required in each case. 

Construction of rules (Basic age, Key date, MDT., HC. 56-67). 

Contra= Contradiction of what is assumed to be correct. 

Council=oi Nicea, AD. 325, (NO.) of Chalcedon, AD. 534 (AM, OS.). 

Chronological Cycles. For the Westerns, divide the year JP. by the circle 19 for 
GN. or Lunar Cycle, or by the circle 28 for Solar Cycle, or by the circle 15 for In- 
diction, and R=year of the cycle. For the Russo-Greek cycles, substitute the year 
AM. for the year JP. Or for the Western lunar cycle, add one to the year AD., 
and divide S by the circle 19. Examples in all almanacs. 

Culminate= upper transit. 

Cycle= Number of years when zero returns to the same date (Chronological). 

D=Date at the end of GND. 

DAGND. and DDGND.= Declination Ascending and Descending=Moon's As- 
cending and Descending Node on the equator. (Equinox.) 

2 



APPENDIX. 

Day 1 to 7=Ferials i to vii=days of the week Sunday to Saturday. Decimals 
of a day (Hours). 

Days Ecclesiastic. Advent Sunday = 4th before Christmas, and the first is the 
Sunday which is nearest to Nov. 30. Agatha=Feb. 5. Agnes=Jan. 21. Alban=: 
June 17. All Hallows=All Saints=All Dead=Nov. 1. All Souls=Nov. 2. 
Alphege=April 19. Ambrose=April 4. Andrew=Nov. 30; Anne = July 26. 
Annunciation = March 25=beginning of the year in CP 

Ascension = Holy Thursday =39 days after Easter. Ash Wednesday — beginning 
of Lent=54 days before Easter. Assumption = Aug. 15. Augustine CD. Aug. 
28. Augustine of England May 26. Barnabas June 11. Bartholomew Aug. 24. 
Bean. O. Sapientia Dec. 16. Bede=May 27. Benedict=Mar. 21. Blasius=Feb. 
3. Boniface June 5. Britius Nov. 13. Candlemas =Purification=Feb. 2. Carl, 
or Care, or Passion Sunday=5th Sunday in Lent=2d Sunday before Easter. 
Catharine = Nov. 25. Cecilia=Nov. 22. Cedde or Chad=Mar. 2. Christmas= 
Dec. 25. Circumcision = Jan. 1. Clement=Nov. 23. Conversion of St. Paul= 
Jan. 25. Corpus Christi= Thursday after Trinity Sunday. Crispm=Oct. 25. 
Cross=Sept. 14. Cyprian=Sept. 26. David=Mar. 1. Dennis=Oct. 9. Dun- 
stan=May 19. Eastern Sunday next after the ecclesiastical full moon, which falls 
on or next after the 21st March in NS., or in OS. In 1864 the Greek Easter 
fell rive weeks later than the Western Easter. Edmund A.B.=Nov. 20. Ed- 
mund, King, Nov. 20. Edward the Confessor = Oct. 13. Edward, King of the 
Saxons=March 18, and Translation = June 20. Ember days = Wednesday, Friday, 
Saturday after 1st Sunday in Lent, and after Pentecost, and after 14th Sept. and 
15th Dec. And Ember weeks are the weeks which contain those days. Epiphany= 
Twelfth day Jan. 6. Ethelred Oct. 17. Eucharist = Easter. Enarchus Sept. 17. 
Eve or Yigil is the day before a feast. Exaltation of the Holy Cross Sept. 14. 
Fabian Jan. 20. Faith Oct. 6. Fourth day of a feast is the 3d day after. George 
April 23. Giles Sept. 1. Good Friday is in Passion week and Friday before 
Easter. Gregory March 12. Hallows, or Hallowsmas, or All Hallows, or All 
Saints Nov. 1. Hilary June 13. Holy Cross May 3. Holy Innocents Dec, 28. 
Holy Rood or Exaltation of the Holy Cross Sept. 14. Holy Thursday or Ascen- 
sion. Hugh Nov. 27. Innocent Dec. 28. Invention of the Holy Cross May 3. 
James July 25. James and Philip May 1. Jerome or Hierome Sept. 30. Jesus- 
name of, Aug. 7. John Dec. 27. John Baptist — beheading of, Aug. 29. Ditto 
Nativity, called Midsummer, June 24. John the Evangelist ante Portam Latinum 
May 6. Jude and Simon Oct. 28. Katharine Nov. 25. Lady — our, see Mary. 
Lambert Sept. 17. Lammas Aug. 1. Laurence Aug. 10. Lent begins with Ash 
Wednesday. Leonard Nov. 6. Low Sunday is next after Easter. Lucian July 8. 
Lucy Dec. 13. Luke Oct. 18. Machatus Nov. 15. Margaret July 20. Mark 
April 25. Martin Nov. 11, and Translation of, July 4. Mary — Conception of, Dec. 
8, and Nativity Sept. 8, and Annunciation March 25, and Visitation July 2, and 
Purification Feb. 2, and Assumption or Death Aug. 15. Mary Magdalene July 22 ; 
Matthaias Feb. 24. Matthew Sept. 21. Maundy-Thursday is next before Good 
Friday. Michael and all angels Sept. 29. Midlent is 4th Sunday in Lent Mid- 
summer is John Baptist's Nativity June 24. Morrow of a feast is the day after. 
Nativity Dec. 25. Nicomed June 1. Nicholas Dec. 6. Octave or Utas of a feast 
is the 7th day after. Palm Sunday is first before Easter. Paschal Sabbath is 
Easter. Passion Sunday is Carl Sunday, and Passion Week is next before Easter 

3 



APPENDIX. 

Paul's Conversion June 25. Paul at Rome July 6. Pentecost or Whitsunday is 
7 weeks after Easter. Perpetua Mauritan March 7. Peter June 20 ; In Cathedra 
Feb. 22 ; at Rome Jan. 18 ; in Yincula or Lammas day Aug. 1. Philip aud James 
May 1. Powder or Gunpowder Plot Nov. 5. Prisca Jan. 18. Purification Feb. 
2. Quadragesima is first Sunday in Lent, is 6 weeks before Easter. Quinquagesi- 
ma or Shrove Sunday is 7 weeks before Easter. Quinziane, or Quinsime, or Quin- 
disme is one week before and after Easter. But in all other cases it begins with 
the feast and extends to two weeks after. Relick Sunday is July 9 to 15, or the 
third Sunday after Midsummer day. Remigius Oct 1 . Richard April 3. Rogation 
days are Monday, Tuesday, Wednesday after Rogation Sunday, which is 5 weeks 
after Easter. Saints — All or All Hallows Nov. 1. Septuagesima and Sexagesima 
are 9 and 8 weeks before Easter. Shrove Tuesday is next before Ash-Wednesday, 
and next after Shrove or Quinquagesima Sunday. Sylvester Dec. 31. Simon and 
Jude Oct. 28. Stephen Dec. 26. Swithun July 25. Thomas Dec. 21. Transfigura- 
tion Aug. 6. Trinity Sunday is 8 weeks before Easter. Valentine Feb. 14. Vigil, 
see Eve. Vincent June 22. Whitsunday or Pentecost. (Wheatly, Missal, Bond, 
CP. 1752.) Some customs depend upon these days. The English terms of Court 
and of the Universities are given in ecclesiastical days. And the great Derby races 
in England are on the 7th Wednesday after Easter. And the writer can identify 
the date Nov. 1, 1887, in Venice, from the ceremonies "Pour toutes les morts," or 
All souls. For Hebrew ecclesiastical days see the calendar HC. 

DDGND. (DAGND.) 

Dionysian Period=KD. and BC=our ordinary dates, and so called because pro- 
posed by Dionysius Exiguus. First used AD. 525. But the Russo-Greeks (AM.) 
used AM. until AD. 1725. 

DJP. Bide 1st. For Days in the Julian Period : Reduce the date in any Era to the 
year JP., and Jan. Cal. OS. Then subtract 2 from the year JP., and divide 1st R 
by 4 for Q and 2d R. Then multiply Q by 1461 and 2d R by 365. Then to these 
two products add the constant 335 and the day of Jan. OS., and S=DJP. (MDB.; 
AE.; ME., NE., OE.) 

DJP. Rule 2. To reduce : Subtract 365 from DJP. Divide 1st R by 1431 for 1st 
Q, and 2d R. Divide 2d R by 365 for 2d Q and 3d R= Jan. Cal. OS. Then mul- 
tiply 1st Q by 4, and to P add 2d Q, and the constant 2, and S=year JP. Then 
by Jan. Cal. table reduce Jan. Cal. to Month Cal. (MDB.; NE.; AE.; ME., OE.) 

Dominical is the Sunday letter for the year JC. 1,2, or 3, but for part of the year 
in JC. 0. And every date which has its Sunday letter the same as the Dominical 
for the year is Sunday that year— Sunday is the same absolute day in all calendars. 
The Sunday letters are the same. But the same day has different dates iu OS. and 
in NS. Hence the Dominicals are different. The rules for Dominicals OS. are 
given in OS. , and for Dominicals N3. are given in NS. And memorized rules for 
Dominicals NS., and for Sunday letters in AC. Rules 9, 10. They are found op- 
posite to the year of the Solar Cycle NS. and OS. And this year for both is found 
by the rule for Chronological cycles. (Solar Cycle.) 

^^Embolismic year of 13 months (HC; HCM.). 

Easter is Sunday next after the full moon which falls on or next after the vernal 
equinox according to the Paschal Canons. This date is represented by the date of 
GN. NS., and of GN. OS. (NS., OS., AM., AC, MDC). It can be easily mem- 
orized (AC Note 71). 

4 



APPENDIX. 

Ecliptic is the apparent path of the sun among the stars (Equinox, Zodiac, Sign, 
Precession). 

Egyptian year=AE., NE. (C). Egyptian cycles (AC, JE. Table). 

Embolismic month = 13th month in a lunar year, and Embolismic year = a lunar 
year of 13 months (E., HC, HCM., OE., AC). And a lunar year of 355 days in 
the Turkish calendar (ME.). 

Epactz=l0.882,932 days in MDC, MDT.=the difference between 12 lunations of 
29.530,589 days, and a Julian year of 365.25 days. In astronomic general terms, 
it is what the greatest number of revolutions within the year falls short of 365.25 
days. The Egyptian epact (AC Rules, MDC). Epacts used by the Church of 
Rome (JE. Table, AC Notes 29, 30, 61, 120-130 ; NS. Table VII.). It is called 
the Lunar Base in AM.). 

Equator =the great circle equi-distant from the poles of the earth. 

Equinox Vernal =VGN., and the zero of solar dates (MD.). VGND. falls about 
March 20, when the sun coming north and apparently revolving in the path of the 
ecliptic crosses the equator at the " equinoxial point," or " First point of Aries." 
From this point the position of each heavenly body is calculated in longitude east- 
ward along the ecliptic, and in latitude north or south of the ecliptic, and this is 
reduced to right ascension (AR.) counted eastward from the same point, and re- 
duced to sidereal time, and declination or angle north or south of the equator. To 
facilitate the calculation, this point is assumed to be fixed. But like a top slowly 
revolving about the pin, while rapidly revolving on its centre, so the pole of the 
earth is slowly revolving about the pole of the heavens, and our North Star is far 
distant from Thuban or a Draconis, which was the North Star about 4600 years ago. 
This causes the equinoxial point to move westward along the equator among the stars 
at the rate of the semi-diameter of the sun in about 19 years, or a full circle in about 
25,000 years. And since AR. is counted eastward, this western movement of the 
equinox is called " The precession of the equinoxes." Hence, stars which are ab- 
solutely fixed are counted as moving eastward, and "The first point of Aries" of 
calculation is about a sign of the zodiac or 30 degrees west of the beginning of the 
constellation Aries. And so of the other signs of the zodiac. This was first dis- 
covered by Hipparchus (Long, 1331). 

Equinoxial year =mean year =365. 242, 216 days. 

Era=KC, AE., AM., AU., HC, HCM., JE., ME., NE., NS., OE., OS. (C). 

Examples are given to illustrate the rules. The rules found elsewhere are fre- 
quently obscure for want of examples. 

February Cal. has Feb. 29 in a leap year or second Feb. 24 in a bissextile ;= JC 0. 
But in Julian time (Min. or Max.), February has no intercalary and all the years= 
865 25 days (Jan. Min.) 

Ferial=Day of the week, I. to VII. = Sunday to Saturday. The Greeks number 
the days I. to V. Then Paraskeue=day of " preparation "= Friday, and Sabba- 
ton— Saturday (Dominical, HC. Rule 7). 

FGND. =Full moon, GND. Astronomic in MD. But to distinguish the eccle- 
siastical full moons of Nisan, NS. FGND. and OS. FGND. are used in MDC. 

First point of Aries (Precession, Zodiac, Equinox). 

Fractions of a day (Hours). 

Full ratf<m=FGN. 

#.=Getrad=III. .9. .204=Hebrew numeral (HC. rule 3). 

5 



APPENDIX. 

GN.= Golden Number=the year of any cycle, and in VGN. only represents the 
year. Originally this term was applied to the numbers I. to XIX. on the marble 
calendars of the Romans, which were gilt to distinguish them as years of the lunar 
cycle, and placed opposite to the dates on which the 235 new moons fell in each 
cycle of 19 years (AC, JE.). 

GNA.= Greenwich Nautical Almanac. 

GJS T . A3f.=GN. found from AM., the Greek year of the World. 

GiVZ>.=Date of zero in that GN. 

GK HC.=GT$. of the Hebrew Calendar (HC). 

GN. JP.=GK found from JP., as GN. NS. ; and GN. OS. And all astro- 
nomical GK are GN. JP. 

GN. i?wfes= Egyptian rules (AC. Rules). 

Great lunar cycle=6501 years, in which the 235th moon represented by any GN. 
advances a full lunation of 29.530,589 days, and the 234th moon falls at the same 
equinoxial date that the 235th moon did 6501 years before that date. NS. Table 
II. makes it 6977 years. AM. and HC. and OS. make it infinite (MDT., Mosaic 
Explanation, HCM., AC). 

Greek (AM.). » 

Greenwich, near London, in England, has recently been agreed upon as the uni- 
versal prime meridian, from which to count longitude and standard time from 
midnight, by all except the French delegates. Hence Stand. = counted from 
midnight at Greenwich. And in the U. S. A. the local standard is becoming gen- 
eral, to make no change except for hours, by subtracting one hour for each 15 de- 
grees of longitude from Greenwich, so that all chronometers shall show Greenwich 
time counted from midnight (instead of nautical time from noon), and all local 
time in U. S. A. will show the same minutes as the chronometers, and differ only 
in the hours. And at the present date (April, 1885) time is kept the same from 
Boston to Charleston, or 5 hours less than Stand. 

Gregorian Calendar=NS. (NS, Introduction). 

Hagion Pascha—Greok Easter (AM., Dominical, MDC). 

Hebrew Calendar =HC, HCM. 

Hebrew time. Add 0.348,148 to Stand. 

Heliacal rising. Long (sec 1329) says that the smallest stars cannot be seen dur- 
ing twilight, or unless the sun is 18 degrees below the horizon. Those of the 6th 
magnitude require the sun to be depressed 17 degrees. Those of the first magni- 
tude require 12 degrees, Mars and Saturn 11 degrees, Jupiter and Mercury about 
10, and Venus not above 5, and she may often be seen in bright sunshine. In 
many of the old calendars the risings of the stars are given, and this signifies when 
they first become visible in the East before sunrise. 

Hours from decimals of a day. Rule. Multiply the fraction of a day by 24 for 
hours and fraction. Multiply the fraction of hours by 60 for minutes and fraction. 
Multiply the fraction of minutes by 60 for seconds and fraction. 

Hours into decimals of a day. Rule. Divide hours by 24 for quotient of deci- 
mals carried to any extent. And divide minutes by 1440 for quotient. And di- 
vide seconds and fraction by 86,400 for quotient. Collect the quotients. Or use 
the following Hour Table. 



APPENDIX. 



To convert Hours, Minutes, and Seconds into liTo convert Decimals of a Day into Hours, 
Decimals of a Day. Minutes, and Seconds. 



1 

2 

3 

4 

5 

6 

7 

8 

9 

19 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 



Decimals. 



is 



.04164- 

.0833+ 

.1250— 

.1666- 

.2083-- 

.250)-- 

.29164- 

.3333+ 

."750 f 

.4166+ 

.4583+ 

.5009+ 

.5416— 

.5833— 

.6250— 

.6366— 

.7083— 

.7500— 

.7916— 

8338— 

.8750— 

.0166— 

9583+ 

1-000+ 24 
25 
20 
27 
28 
29 



as 



X 



(DO S m 
™ S G * 3 „- 

^2^ M XC3 rt 
~^ 2 ci .--' 

«3 32 d « •*> af 

« cs .2 P <» -« 

!_« +5 " S3 72 



131 

132 
33 
34 

!35 

| 36 
37 
38 

| 39 
40 
41 

i42 
43 

144 
45 
46 
47 
48 
49 
5 J 
51 
52 
53 
54 
55 
56 
57 
58 

!59 

!60 

I 



Decimals. 



.000,691+ 

.001,388 + 

.002,083— 

.002,777 

.003,472 

.004.1064- 

.004,861 

.0)5,555 

.006,25 ) 

.006 944 

.007.638+ 

008,333+ 



.009,027+ 13 

.009,722+ 

.010,416+ 

.OJ 1,111 

.011,805 

.012,500 

.013,194+ 

.013,888 

.014,583 

.015,277— 

015 97: 

.016,666 

.017,361 

.018,055 

.018,759 

.019,444 

.020,138 

.020,833 

.021,527 

.022,222- 

.022|916- 

.023,611— 

.024,305 

.025,000 

.025 694 

.026,388 

.027,083 

.027.777— 

.028,472+ 

.029,166 

•029,861— 

.030,555 

.031,250 

.031.9444- 

.032,638 

.033,333 

.034,027— 

.034,722 

.035,416 

.036,111— 

.030,805— 

037.500 

.038,194— 

.038,888 

.039,583 

.040,277— 

.040 972 

.041,666— 



14 
15 
16 

17 
18 

19 
20 

21 
22 
23 
2-1 
25 
26 
27 
2s 
29 
30 
31 
32 
38 
34 
85 
8(3 
37 
88 
39 
40 
41 
42 
18 
44 
45 
46 
47 
48 
49 
50 
51 
r>^ 
53 
54 
55 
50 
57 
58 
59 
60 



Decimals. 



.000,011,6 
.000,023,1 
.000,034,7 
.009,046,3 
.000,057,9 
.000,060,4 
.000,081,0 
.000,092.5 
.000,104,2 
.000,115,7 
.000,127,3 
.000,188,9 
.000,150,5 
.000.162,0 
.000,173,6 
.000,185 2 
.000,196,8 
,000,208,3 
.000 219,9 
900,231,5 
•000,243,1 
.000,254,6 
.000,266,2 
.000 277,8 
.000,289,4 
000,300,9 
.000,312,5 
.000,324,1 
.000,335,6 
.000,347,2 
.000,858 8 
.0)0,370,4 
.000,381,9 
.000,393.5 
.000,405,1 
.000,416,7 
.000,428,2 
.000,439,8 
.000,451,4 
.000,403,0 
.000,474.5 
.000,486,1 
.000,497,7 
.000,509,3 
.000,520,8 
.000.532,4 
.000,544,0 
.000.555,6 
.000,567,1 
.000,578,7 
.000,590,3 
.000 601,9 
.000,613,4 
.000,625,0 
.000,63(5 6 
.000,648,1 
.000,659,7 
.000,671,3 
.000,682,9 
.000,694,4 



.01 

.02 

.08 

.04 

.05 

.06 

.07 

.08 

.09 

.10 

.11 

1.2 

.13 

.14 

.15 

.16 

.17 

.18 

.19 

.20 

.21 

.22 

.23 

.24 

.25 

.26 

.27 

.28 

.29 

.39 

.31 

.32 

.33 

.34 

.35 

.36 

.37 

.38 

.39 

.49 

.41 

.42 

.43 

.44 

.45 

.46 

.47 

.48 

.49 

.5 J 

.51 

.52 

.53 

.54 

.55 

.56 

.57 

.58 

.59 

.60 



M. S. 



14 
28 
43 
57 
12 
26 
40 
55 
9 
24 
38 
52 
7 
21 
36 
50 
4 
19 
33 
48 
2 
16 
31 
45 

14 
28 
43 
57 
12 
26 

40 

55 
9 

24 

38 

52 
7 

21 

36 

50 
4 

19 

33 

48 
2 

16 

31 

45 


14 

28 

43 

57 

12 

26 

40 

55 
9 

24 



24 
48 
12 
36 

24 
48 
12 
36 

24 
48 
12 
36 

24 
48 
12 
36 

24 
48 
12 
36 

24 
48 
12 
36 

24 

48 
12 

36 


24 

48 

12 

36 


24 

48 

12 

36 


24 

48 

12 

36 


24 

48 

12 

36 


24 

48 

12 

36 




.01 
.62 

.68 
.64 
.65 
.63 
.67 
.68 
.69 
.70 
.71 
.72 
.73 
.74 
.75 
.76 
.77 



.81 
.82 
.83 
.84 
.85 
.86 
.87 
.88 
.89 
.90 
.91 
.92 
.93 
.94 
.95 
.96 
.97 
.98 
.99 



n. M. 



14 38 24 



52 

7 



16 



16 48 

17 2 



.001 
.002 
.003 
.004 
.005 
.006 
.007 
.008 
.009 
.010 



21 36 



15 36 
15 50 24 



16 19 12 

16 33 36 


24 

17 W 48 
17 31 12 

17 45 c:6 

18 
18 14 24 
18 28 48 
18 43 12 

18 57 36 

19 12 
19 26 24 
19 49 48 

19 55 12 

20 9 36 
20 24 
20 38 24 

20 52 48 

21 7 12 
21 21 36 
21 36 

21 50 24 

22 4 48 
22 19 12 
22 33 36 

22 48 

23 2 24 
23 16 48 
23 31 12 
23 45 30 



1 26.4 

2 52.8 

4 19.2 

5 45.6 

7 12-0 

8 38.4 

10 4.8 

11 31.2 

12 57.0 
14 24.0 



.0001 
.0002 
.0003 
.0004 
.0005 
.0006 
.0007 
.0008 
.0009 
.0010 



8.64 
17.28 
25.92 
34.56 
43.20 
51-84 
60.48 
69.12 
77.76 
8640 



APPENDIX. 

Ides, in the Roman year (JE., AIL), fell on the 18th of Jan., Feb., April, June, 
Aug., Sept, Nov., Dec, and on the 15th of March, May, July, Oct. And the 
nones fell 8 days before the Ides, or on the 5th when the Ides fell on the 13th, and 
on the 7th when the Ides fell on the 15th, as we count (JE. Table). 

Index number in NS. Tables II., III., and in AC. Tables II., III., gives the 
number of days after March 21, NS., on which falls the date of GN. 3, as the 
standard (AC, NS.). 

Indiction. The year of Indiction found by the rule for Chronological cycles is 
the same year of the Roman and of the Greek cycle. It began AD. 313. 

Initials of the words signified are used as symbols. 

Intercalary =Feb. 29 in a leap year, and second Feb. 24 in a bissextile. The 
year NE. had 12 months of 30 days, and at the end 5 intercalary days called Epag- 
omcnai. The year AE. was a modification of NE., and had a sixth Eipagomenas 
added in the same years as the Roman Bissextile (AE., NE., JE.). 

Iphitus (OE.). 

Jach=18 hours=Hebrew numeral (HC). Changed to 10 hours in HCM. (HC. 
Rule 3). 

Jan. Col. Table. 0+Jan.; 31+Feb.; 59 (60)+March ; 90 (91)+ April ; 120 (121) 
-1-May; 151 (152)+ June ; 181 (182)+ July ; 212 (213)+ Aug.; 243 (244)+ Sept.; 273 
(274)+Oct.; 304 (305)+ Nov.; 334 (335)+ Dec. 

Rule 1. To find the day of January in Calendar time, add the given day of the 
given month to the number prefixed to that month in the table, using the smaller 
number in JC. 1, 2, 3, but the larger number in JC. or leap year. 

Or by memory. Add together all the days in the previous months and the given 
day of the given month, counting February=28 days in JC. 1, 2, 3, but 29 days in 
JC. 0. (Jan. Min.) 

Rule 2. To reduce Jan. Cal. Subtract the next smaller number in the table 
(using the smaller number in JC. 1, 2, 3, but the larger number in JC. 0) and R= 
day of the month Cal. to which that number is prefixed. 

Or by memory. Add together the days in the successive months (counting Feb. 
=28 days in JC. 1, 2, 3, but 29 days in JC. 0) until the sum is next less than Jan. 
Cal. Then subtract S from Jan. Cal. and the remainder = day of the month Cal., 
next after the month added to the sum. 

Rule 3. Use Jan. min. table as it stands in JC. 1, 2, 3, but in JC. 0, count Jan. 
one day more or day of the month one day less, on and after March 1. 



APPENDIX. 


















£ 

1 


JAN. MIN. TABLE. 


1 

s 


03 
0J 


o 

5 




50 


1 


>> 

"3 


02 

Sic 
pi 


a 

4) 

"S, 


o 


5 
o 

> 
© 


© 

1 


s 


£ 


£< 


a 


< 


S 


i-a 


HS 


<, 


03 


o 


£ 


R 


1 


1 


32 


60 


91 


121 


152 


182 


213 


244 


274 


305 


335 


2 


2 


33 


61 


92 


122 


153 


183 


214 


245 


275 


306 


336 


3 


3 


34 


62 


93 


123 


154 


184 


215 


246 


276 


807 


337 


4 


4 


35 


63 


94 


124 


155 


185 


216 


247 


277 


308 


338 


5 


5 


36 


64 


95 


125 


156 


186 


217 


248 


278 


309 


339 


6 


6 


37 


65 


96 


126 


157 


187 


218 


249 


279 


310 


340 


7 


7 


38 


66 


97 


127 


158 


188 


219 


250 


280 


311 


341 


8 


8 


39 


67 


98 


128 


159 


189 


220 


251 


281 


312 


342 


9 


9 


40 


68 


99 


129 


160 


190 


221 


252 


282 


313 


343 


10 


10 


41 


69 


100 


130 


161 


191 


222 


253 


283 


314 


344 


11 


11 


42 


70 


101 


131 


162 


192 


223 


254 


284 


315 


345 


12 


12 


43 


71 


102 


132 


163 


193 


224 


255 


285 


316 


346 


13 


13 


44 


72 


103 


133 


164 


194 


225 


256 


286 


317 


347 


14 


14 


45 


73 


104 


134 


165 


195 


226 


257 


287 


318 


348 


15 


15 


46 


74 


105 


135 


166 


196 


227 


258 


288 


319 


349 


16 


16 


47 


75 


106 


136 


167 


197 


228 


259 


289 


320 


350 


17 


17 


48 


76 


107 


137 


168 


198 


229 


260 


290 


321 


351 


18 


18 


49 


77 


108 


138 


169 














19 


19 


50 


78 


109 


139 


170 


200 


231 


262 


292 


823 


353 


20 


20 


51 


79 


110 


140 


171 


201 


232 


263 


293 


324 


854 


21 


21 


52 


80 


111 


141 


172 


202 


233 


264 


294 


325 


355 


22 


22 


53 


81 


112 


142 


173 


203 


234 


265 


295 


326 


356 


23 


23 


54 


82 


113 


143 


174 


204 


235 


266 


296 


327 


357 


24 


24 


55 


83 


114 


144 


175 


205 


236 


267 


297 


328 


358 


25 


25 


56 


84 


115 


145 


176 


206 


237 


268 


298 


329 


359 


26 


26 


57 


85 


116 


146 


177 


207 


288 


269 


299 


33 U 


360 


27 


27 


58 


86 


117 


147 


178 


208 


239 


270 


300 


331 


361 


28 


28 


59 


87 


118 


148 


179 


209 


240 


271 


301 


332 


362 


29 


29 




88 


119 


149 


180 


210 


241 


272 


302 


33:3 


363 


30 


30 




89 


120 


150 


181 


211 


242 


273 


303 


334 


364 


31 


31 




90 




151 




212 


243 




304 




365 



Jan. Jfm.=Day of Jan- 
uary in minimum Julian 
time. 

Jan. Min. Rule 1. For 
month Cal. find the date of 
Zero, in terms of Jan. min. 
by MDT. Then in Jan. min. 
table, find month min. oppo- 
site to Jan. min. Then to 
month min. add JCC. for 
month Cal. And if this make 
as much as Dec. 32, then sub- 
tract 31 to find the day of 
January of the next year. 
And for month min. JCC.= 
0.00 in JC. after Jan. 59, 
but JCC. =1.00 in JC. be- 
fore Jan. 60; and JCC. =0.25 
in JC. 1 ; and 0.50 in JC. 2, 
and 0.75 in JC. 3. 

Thus. In JC. 0, Jan. min. 
59 and 60=Feb. min. 28 and 
March min. lst=Feb. Cal. 
29 and March Cal. 1st. And 
in JC. 3; Jan. min. 365.900 
=Dec. min. 31.900 ;+0.75 
JCC.=Dec. Cal. 82.65=JC. 
Jan. Cal. 1.65. 

Jan. Min. Rule 2. For Jan. 
Cal. By MDT. find the date 
of zero in terms of Jan. min. Then for Jan. Cal. add JCC. as for month Cal. ex* 
cept in JC. 0, count JCC. =1.00 for the whole year. Then prove the calculation by 
finding precisely the same date by MDB. Then in Jan. min. table find month Cal. 
opposite to Jan. Cal. except in JC. 0, after Jan. 59 take Month Cal. one day less. 

Thus : In JC. 0, MDT. makes full moon AD. 1288, Jan. min. 71.836,594. Add 
1.00 JCC. = Jan. Cal. 72.836,594 as found by MDB. opposite to March 13=March 
12.836,594. 

Jan. Min. Rule 3. In terms of Jan. min. Add or subtract mean revolutions to 
any extent in years of 365.25 days, and find the result by Rule 1 or 2. 

Thus : JC. Jan. min. 60, +365 ;-^365.25 leaves Jan. min. 59.75 in JC. 1. Then 
for Jan. Cal. add 0.25 JCC. = Jan. Cal. 60. This is the same as in JC. 0, and 
March 1 in JC. 1 is 365 days after March 1 in JC. 0. 

Jan. Min. Rule 4. By memory. Add together the days in the previous months 
and the given day of the given month and the sum will be Jan. min. if February 
be always counted 28 days. 

Jan. Min. Explanation. The Julian year of calculation =365. 25 days. It has no 
intercalary Feb. 29, but makes 1461 days in 4 years, by adding 0.25 to the end of 
Dec. 31 of each year. Then, in JC. 0, March 1st is Jan. 61 in calendar time, but 

9 



APPENDIX. 

Jan. 60 in Julian time, or one day less, and hence minimum. Then taking JC. ' 
March l=Jan. min. 60 as the standard, JCC.=0.00 to the end of Dec. 31. Then 
the addition of 0.25 carries Jan. min. to Jan. Cal. 1.25 in JC. 1, then to Jan. Cal. 
1.50 in JC. 2 ; and to Jan. Cal. 1.75 in JC. 3 ; and to Jan. Cal. 2.00 in JC. 4 or 
JC. 0. And Jan. min. falls one day moie than Jan. Cal. in JC. 0, until Jan. Cal. 
throws in the intercalary, Feb. 29 in a leap year, and makes them the same. Then 
Jan. min. 60=March min. lst-f 0.00 JCC.=March Cal. 1st as at first 

But by Rule 2, When counted in the day of Jan. March 1st in JC. 0= Jam 61, 
so that in JC. 0, JCC.=1.00 for the whole year. 

JC. Rule. For the year of the Julian cycle of 4 years, counting leap year or bis- 
sextile=JC. 0. Subtract nothing from the year AD., but subtract one from the 
year JP., and BC, and HC, and JE. Then divide R by 4 and second R=0, 1, 2, 3 
=JC. 0, JC. 1, JC. 2, JC. 3. And count JC. 0=JC. 4 before Feb. 29. (Jan. Min.) 

JCO. Rule. For JC. correction. Multiply JC. by 0.25. (Jan. Min.) 

JE'.= Julian Era = Julian Calendar. (C.) Also Julian Equation. (MDK., MDC, 
MDT.) Jewish Calendars. (HC, HCM.) 

JP.= Julian Period. Rule. To find the year JP. (=AJP.) add 4713 to the year 
AD., or subtract the year BC. from 4714. And to reduce JP., subtract 4713 for 
the year AD. or subtract the year JP. from 4714 for the year BC. For other 
calendars the rules are there given. (C.) 

JP. GLZV.=GN. found from JP.=all astronomical GK And GT$. NC, GN. 
OS., and GN. NS. But these can be thus found : Add one to the year AD., and 
divide S by the circle 19 and R= JP. GN. 

Julian Period= JP. This is an artificial calendar as a universal standard for 
dates in all calendars, through which a date in one calendar can be transformed 
into the date in any other calendar, or dates from all calendars can be retained as 
dates JP. to be compared. It is so called from its resemblance to the Julian Calen- 
dar (JE.). It is calculated backwards until the year 1 of the three western Chron- 
ological cycles meet in the same year=JP. 1. And counted backwards from JE. 
1=BC. 45= JC. 0=Bissextile, it makes JP, 1=JC. 0. And beginning with JP. 1 
=JC. 0, it counts every fourth year thereafter as a bissextile or a leap year. 
Counted forwards it makes JE. 1=BC. 45= JC. and every fourth year thereafter 
a bissextile or a leap year, and therefore is uniform, while the Romans through 
error, did not put the intercalaries in the same years as JP. after BC. 45 until 
AD. 4. And AD. 1 was the first regular year after this confusion (JE.). Hence 
all calculations for indefinite periods are in OS. carried back to JP. 1. Because 
before NS. Introduction, each fourth year was a leap year or a bissextile. The 
Russo-Greeks still retain OS., and their leap years count every fourth year from 
BC. 45 as if JE. had been counted regularly. The irregularities of NS. are then 
thrown in by adding NS. SC. 

Scaliger, who introduced this use of JP. , has been charged with plagiarism, 
because AM., "the Constantinopolitan Period," like JP., makes AM. l=year 1 of 
all the Greek Chronological cycles. But Scaliger does not claim that he invented 
this short mode of finding the years of the cycles. His improvement was the use 
of JP. as a common standard of dates. And although the Metropolitan of Kiev, 
in his " Full Christian Calendar," in Sclavonic text with Arabic numerals (AM. ), 
gives the year AM. with its corresponding years of the three cycles, still its use 
appears to be so little known among the Greeks, that the author of a Greek « ' Book 

10 



APPENDIX. 

of the Litany " takes three pages for the rules to find the years of the three Greek 
cyles. These works were lent to me by "Father Agapius," with a manuscript 
Greek translation of the Sclavonic text. 

Julian time is counted by Julian years. (Jan. Min.) 

Julian ycar=SQ5.25 days. (Jan. Min.) 

Kalends. (Calends ; JE. Table)=: First day of the month in AU. and JE. 

Key Bate— standard date from which to determine the date of each GN. in the 
cycle. In all cases add an epact to the date of GN. 1 and S=key date. (MDC; 

AC. Notes.) 

Key Epact is analogous to Key date. (AC. Rule 5.) 

LAGNB.— Latitude Ascending GND., as LDGND.= Latitude Descending 
GND.=date of the moon's Ascending and Descending node upon the ecliptic. 
(DAGND. ; Equinox.) 

Latitude in the heavens = angle North or South of the Ecliptic, while Declination 
is angle North or South of the equator. (Equinox.) 

LC.= Lunar Correction. (NS.) 

LBGNB. (LAGND.) 

Leap year= JC. 0, with the intercalary Feb. 29, as Bissextile =JC. with the in- 
tercalary between Feb. 24 and 25. And to find JC. 0, subtract nothing from the year 

AD. or AM., but subtract one from the year BC, or JP., or JE., or HC. Then 
divide R by 4, and if there be no remainder, the year= JC. 0, invariably in calcula- 
tion=date OS. But through error the Romans counted the wrong years. And 
NS. counts as common years all centurial years AD. which leave any remainder 
when the centuries are divided by 4, as AD. 1700, 1800, 1900, 2100. 

Local Almanacs give local time, on the basis of standard time given in the nauti- 
cal almanacs. The rise and set of the heavenly bodies vary with the latitude as 
well as the longitude. (MDE. ) 

Local time. Rule. Multiply the degrees of longitude from Greenwich by 0.002,778, 
and minutes by 0.000,046 ; and seconds and fractions by 0.000,001, and the sum= 
fraction of a day to be added to standard time if the locality be East or subtracted 
if West. 

Or : Multiply degrees by 4 minutes, and minutes by 4 seconds, and seconds and 
fraction by 0.066 for seconds and fraction, and the sum will be the difference in 
time. 

Or : If longitude be given in time find the fraction of a day by the Hour table. 

Examples in which + =East, and — =West : 



LOCALITY. 


H. .M..S. 


FRACTIONS. 




Babylon 

Mecca 

Jerusalem 

Alexandria 


+2.. 56.. 39 
+2.. 40.. 32 
+2.. 21.. 20 
+2.. 1.. 4 
+1..35..28 
+0..49..54 
0.. 0.. 
-5.. 00.. 00 


+0.122,674 
+0.111,481 
+0.098,148 
+0.084,074 
+0.066,296 
+0.034,653 
0.000,000 
—0.208.333 


MD. 2d Ex. 

ME. 

HC, HCM., AC. 

AC. Note 83. 


Athens 


MD. .4th Ex. 


Rome 


JE. Note 3. 


Greenwich 


Standard ; Prime. 


75 degrees West 


Local Standard. 







11 



APPENDIX. 

Zow=Longitude (Local). 

Lunar Z?«s£=Epact (AM.). 

Z (7.= Lunar Correction (NS.) 

Lunar Cycle— 235 lunations in 19 years. (Great.) 

Lunation= Synodic revolution of the moon, from full to full or from new to 
new =29. 530, 589 days. (MD.; MDB.; MDC, MDE.; MDT.) 

March 21 in OS. and NS. and AC, is the ecclesiastical date of the vernal equinox 
(AC. Notes 1-16.) 

3Iax.= Maximum Julian date=latest date when counted by day of the month 
after Feb. 29=Cal. in JC. 3. For max. Hebrew date add 1.098,148 to min. stand., 
i. e. add 0.75 JCC. for max. stand., +0.098,148 for longitude of Jerusalem, +0.25 
to count from 6 hours before midnight. (AC. Notes 12-16, 32, 50, 52, 80, 91.) 
' MD.— First Mean Date, on the basis of a mean year=365.242,216, and standard 
VGND.=AD. 1866 March 20.837,442, Cal., NS., Stand., as the mean between the 
extreme variations of the actual 0.007,582 more and less than the mean, between 
AD. 1866 March 20.. 19 h. . 55 m. and AD. 1870 March 20. .19 h. .32 m. And 
365.242,216 is the estimate of a mean year in GNA. since 1857. In 1856 (p. 581) it 
says: "The equinoxial year has been assumed, according to Bessel (Conn, des 
Temps 1831, Additions page 154), equal to 365.242,217 mean solar days.'*' Delambre 
says that NS. SC. by omitting 3 days in 400 years OS. has an error of one day in 
3600 years. This makes the mean year 365.242,222 days. And Smyth (pp. 83, 115) 
gives 365.242,24] ,4 as the estimate of Baily in 1827. And a mean year of 365.242,216 
makes the summer solstice at Athens JP. 4282 June 27..8h..48 m. after mid- 
night, while Meton estimated it 5 or 6 hours when modern instruments of precision 
were unknown. And this was 2300 years before AD. 1869. (MD. 4th Ex.) (AC. 12.) 

MD. Second. Also, on the basis of a mean lunation =29. 530,589 days and standard 
date of full moon AD. 1853 Sept., 17.993,023 Cal., NS., Stand, as the mean between 
the extreme variations of the actual 0.568,302 more and less than the mean in the 
cycle of variations, from AD. 1853 Sept. 17. .10 h. .12 m. to AD. 1854 March 14. . 
17 h. .53 m. And 29.530, 5S9 reduces to six places of decimals the estimate of Baily 
29.530,588,773,1 as stated by Smyth (p. 121). And it gives the mean date of full 
moon at Babylon JP. 3993 March 19.467,827 counted from midnight, or 0.428,006 
less than the actual date of the eclipse, and this is less than the extreme variations 
0.568,302 in the fundamental cycle of variations. And to make 29.530,588,773,1 the 
standard, find the difference in years between the given year and AD. 1853, and 
multiply this difference by 0.000,002,806,4, and add P. to FGND. if the given year 
be earlier, or subtract if later than AD. 1853. And this would make 0.007,220,867 
or less than 11 minutes to be added to the above date for 2573 years. And the 
above standard date with mean lunations of 29.530,589 makes the mean date of 
conjunction AD. 622 July 14. .1 h. .26 m. which Ideler, the Prussian Astronomer 
Royal, makes AD. 622. .1 h. .12 m., while he gives the actual July 14. .8 h. .17 m. 
(ME.) 

MD. Rule 1. By MDT. find the date of zero in terms of Jan. Min., OS., Stand. 
Then by Jan. Min. reduce the date to Jan. Cal., OS., Stand. Then verify the cal- 
culation by finding the same date precisely by MDB. Then, if desired, add NS. 
SC. for date NS. And add or subtract for Local time. Then, for other dates of 
zero, add or subtract mean revolutions to any extent. And for half zero add or 
subtract half a revolution, except, to the date of the Vernal equinox, add 92.833,33c 

12 



APPENDIX. 



for Summer solstice, or 186.472,222 for Autumnal equinox, or 276.177,778 for Win- 
ter solstice. Then reduce the fraction of a day by the Hour table. 

MB. 1st Ex. FGND. in AD. 1853, Sept. 17.993,023, Cal. NS. stand. =lunar 
standard in MDB., MDC, MDE., and MDT. (MD. Second), 

MB. 2d Ex. FGND. in JP. 3993, March 19.467,827, Cal. OS., at Babylon 
0.122,674, East Local. This is the earliest lunar date on record and the mean date 
of full moon at the eclipse which occurred 2,600 years before AD. 1880 and 114 
years before the Jewish Captivity, as quoted by Tycho Frahe (Prol. 6) from Pto- 
lemy of Alexandria (Aim. Lib. 4, Chap. 6) in terms of NE. at NE. 27, Thoth 29, 
at 9 hours, 30 minutes after noon= JP. 3993, March 19.895,833, or 0.428,006 later 
than the mean (MD, Second ; MDE. 2d Ex.). 

MB. M Ex. VGND.=AD. 1866, March 20.837,442, Cal. NS. Stand. =solaf 
standard in MDB., MDC, and MDT. (MD. First). 

MB. Aih Ex. Summer solstice JP. 4282, June 27.336,919, counted from mid- 
night at Athens +0.066, 296 Local. This is for the earliest solar date on record, 
2300 years before AD. 1869, as given by Tycho Brahe (Prol. 6), as determined by 
Meton and Euctemon, as the limit of the Olympic year (OE.) in terms of the Era 
of Nabonassar NE. 316, Phamenoth 21 at 5 or 6 hours after midnight= JP. 4282, 
June 27 at 5 or 6 hours after midnight, while MD. gives 8 hours, 48 minutes. But 
Meton had no modern instruments of precision (MD. First). 

MB. 5t7i Ex. The above examples are given to prove the rules. They are also 
proved by other historic dates (Zero). 

MBB.— Mean Date by Basic ages, in terms of JP., Jan. Cal., OS., Stand. 

Bide. Assume some date in 
any Era, a few days later than 
the date desired. Reduce this 
assumed date to year JP. and 
Jan. OS and thence to DJP., 
to which add the basic age of 
zero, and divide the sum by the 
revolution of zero to whole 
numbers in the quotient, and 
subtract the remainder from the 
assumed date in any form, and 
the remainder will be the mean 
date of zero in that form in 
terms of Cal. OS. Stand. Then 
as MD. Rule 1. 



CO 




VGN. 




FGN. 






246.701,622 




5.078,489 


_o 








NGN. 


"co 

03 

PQ 








19.843,783 




i 


365.242,216 


1 


29.530,589 


«*-! 


2 


730.484.432 


2 


59.061,178 


o 

CO 


3 


1095.726,648 


3 


88.591,767 


co a 


4 


1460.968,864 


4 


118.122,356 


,-<•.£ 


5 


1826.211,080 


5 


147.652,945 


Ph 2 


6 


2191.453,296 


6 


177.183,534 


Hi 


7 


2556.695,512 


7 


206.714,123 


9(2 


8 


2921.937,728 


8 


236.244,712 


a 


9 

i 
i 


3287.179,944 

(4) 


9 


265 775,301 
(5) 



And to expedite the division, use the multiples of revolutions. And to prove di- 
vision, throw out the 9's in the divisor and quotient, then multiply these re- 
mainders, and to the product add the digits in the general remainder and throw out 
the 9's, and the remainder must be the same as the remainder of the dividend after 
throwing out the 9's. And to throw out the 9's, add together the digits and di- 
vide by 9. Thus 4 is the remainder of 365.242,216, and 5 is the remainder of 
29.530,589 after throwing out the 9's. 

MBB. 1st to Uh Ex., as MD. 1st to 4th Ex. 

13 



APPENDIX. 



MDB. mh Ex. Mean new moon fell AD. 607, Aug. 26. .16 h. .3 m. .4 sec, 
counted in Hebrew time. And HC. makes Moled Tisri fall Aug. 28 . . 16 lioura 
exactly. And there is only one chance in 1080 that the date should by accident 
fall at £ of a day without the difference of a single "scruple" of 3£ seconds (HC. 
Note 125). 

MDB. 6th Ex, In AD. 607, VGND. fell March 19.235,646 in Hebrew time, and 
the full moon March 19.250,589 in Hebrew time, so that the full moon of AD. 607 
had passed the equinox 22 minutes, and had just become the full moon of Nisaru 
And AD. 607=HC. GN. 17, which is the earliest Hence, the lunar and solar 
dates by the present Hebrew Calendar (HC.) indicate that it was constructed about 
AD. 607 (HC. Notes 125, 126). 

MDB. 7tfi Ex. New moon fell BC. 45, Jan. 1.807,962 counted from midnight at 
Rome (Local)=7 hours, 23 minutes after noon. ON. 1 is dated Jan. 1 in the Julian 
Calendar (JE. Table). And History says that the Julian Calendar (JE.) began at 
the date of new moon BC. 45, Jan. 1 (AC. Note 99-101). 

MDB. 8th Ex. AD. 325 new moon Ml March 31.071,421 counted from midnight 
at Jerusalem (Local), or March 31.321,421 in Hebrew time. The Alexandrian cy- 
cle dates GN. 3=March 31. Jarvis (p. 95) says that in AD. 325 new moon fell 
March 23, and was marked GN. 1 (MDT. 5th Ex.). 

A rough calculation showed that this statement by Jarvis did not correspond 
with the historic statement of new moon Jan 1, BC. 45. To determine this ques- 
tion MDB. was constructed. And this was the origin of the present work on Cal- 
endars, and of a manuscript work on Practical Astronomy (PA). (AC. Notes 97- 
101). 

MDC.=Mean Date Condensed. 



In terms of AD., 
NS. for NS. FGN. 



March Min., NS., Stand, for VGN. and NGN. 
and of March OS. for OS. FGN. 



and of March 



Zero. 


Cy. 


Key Date. 


Epaet. 


Revolutions. 


AD. to AD. 


JE. per cycle. 


VGN. 


1 


23.851,186 


0.037,784 


365.242,216 


1800 to 1899 


— 0.007,784 


FGN. 


19 


£5.556,804 


10.882,832 


3& 530,589 


1881 to 1S99 


— 0.061,585 


NS. FGN. 


19 


55 NS. 


11 


30 


1700 to 1S99 




OS. FGN. 


19 


47 OS. 


11 


39 


Forever. 





Then to the date of the Yernal Equinox, add 92.833,333 for Summer Solstice, or 
186.472,222 for Autumnal Equinox; or 267.177,778 for Winter Solstice. 

MDG. Bute 1. Construction. By MDT. find the date of the vernal equinox in 
the centurial year in terms of Jan. Min., OS. Stand. Then add NS. SC, and sub- 
tract 59 for the day of March NS., and record the result March 20.851,186 as the 
key date for AD. 1800 to AD. 1900, when NS. SC. adds one day more. And as 
Its epact record the difference between a mean year of 365.242,216 days, and a Jul- 
ian year of 365.25 days= —0.007,784= JE. in the last column. 

Then for FGN. : By MDT. find the date of GN. 1 of the current cycle in 
terms of Jan. Min., OS. Stand., and add NS. SC, and subtract 59 days for the 
day of March NS. To this date add the epact in MDT. =10.882,932 and S=key 

u 



APPENDIX. 

date, or zero of the cycle, from which zero the date recedes 10.882,932 days per 
year until it becomes too early, when a lunation of 29.580,589 days is added. Re- 
cord this key date, and epact, and revolution, and the first and last year of the cy- 
cle, and the JE. per cycle= —0.061,585, as in MDT. Thus AD. 1881 +4718= JP. 
6594;--19=Q 347+GN. 1. Then 347x0.061,585 from Jan. 113.043,867=Jan. 
91.673,872 OS. ; +12 NS. SC.-59=March 44.673,872 NS., the date of mean full 
moon in AD. 1881, GN. 1. Then add the epact 10.882,932=Marck 55.556,804, the 
key date. 

Then for the ecclesiastical NS. FGN. : To March 24 or 54, add NS. Index of 
the century for the key date, dated NS. And for OS. FGN. make March 47 OS., 
the key date " For ever,'* with epacts 11 days and revolutions 30 days. And mark 
the limits of NS. FGN. at AD. 1700 to AD. 1899, when NS. Index will change 
from one day to two days. (AC. Notes 59.) 

Then copy the table and memorize the rules, for use during the limits, with less 
calculation than by MDT. or MDB., for astronomic dates, and including the eccle- 
siastical dates which are subject to the same rule of key dates. And the insertion 
of JE. per cycle, makes the table perpetual, so that mean dates can be found for 
all time, when the more convenient rules of MDT. and MDB., for dates beyond 
the limits are not at hand. Thus for the day of January add 59 days to the key 
dates. And subtract 12 days for OS., and then add NS. SC. for the century, for 
dates NS. And for VGN. multiply by 0.007,784 the difference between AD. 1800 
and the given year, and add P to the key date if before or subtract it if after AD. 
1800. And for FGN. multiply by 0.081,585 the number of cycles before or after 
the cycle in the table and add P to the key date if before, or subtract it if after the 
same GN. in the table. 

MDC. Bide 2. For VGND. : Subtract 1800 from the year AD.; and multiply R 
by the epact, and subtract P from the key date. 

MDC. Bule 3. For FGND. : Add one to the year AD. ; and divide S by the circle 
19 for R=GN. Then multiply GN. by the epact and divide P by the revolution, 
and subtract R from the key date, and 2d R=date of zero. 

MDC. Bule 4. For NS. FGND. and for OS. FGND.: Add one to the year AD.; 
and divide S by the circle 19 for R=GN. Then multiply GN. by the epact, and di- 
vide P by the revolution; and subtract R from the key date and 2d R=date required, 
if on or between March 21 and 50. If not, then add or subtract 80 days to bring 
the date within the limits. 

MDC. Bule 5. For the date of Easter : By Rule 4. Find NS. FGND. and OS. 
FGND., and Sunday next thereafter is the Greek Easter for ever, and NS. Easter 
during this century. And thus for ever, find OS. FGND., and add NS. SC. and 
the Sunday next thereafter = Greek Easter, dated NS. And in other centuries, if 
NS. FGND. fall on March 50 (April 19) retract it to April 18. And if any GN. 
from GN. 12 to 19 thus fall on April 18, then retract it to April 17. (AC. Notes 
66-70.) 

MDC. 1st Example. The standard mean date of the vernal equinox in all the 
rules of MD.=AD. 1806 March 20.837.442 ; Cal., NS., Stand. (MD. First). Then 
1866-1800=66 ; X 0.007,784=0.513,744 ; from 20. 851, 186= March 20.337,442 ruin., 
in JC. 2. Add 0.50 JCC.=March 20.837,442 Cal., NS., Stand. 

MDC. 2d Example. Mean date of full moon in AD. 1891 ;+l ;-19=GN. 11 ;X 
10.882,932--29.530,589=leaves 1.589,896, which from 55.556,804= March 53.966*908 
min. To which add 0.25 JCC. for Cal. 

15 



APPENDIX. 

Then for date outside of the limits, keep the date in minimum Julian time 
March 53.966,908. Then AD. 1853=GN. 11, at 38 years before 1891=2 cyclesX 
0.061 ,585 +58. 966, 908 =March 54.090,078; then add 5 lunations of 29.530,589= 
Sept. 17.743,023 min. Add 0.25 JCC. = Sept. 17.993,023 Cal., NS., Stand. =stand- 
ard lunar date in all the rules of MD. (MD. Second.) 

MDC. M Example. For the dates of Easter in AD. 1864 ;+l ;-19=GN. 3 ;Xll 
s-30 leave 3 from March 55 NS. =March 52 NS. -30=March 22 NS. And 3 from 
March 47 OS.=March 44 OS., within the limits. Then March 44 OS.+12 NS. SO. 
=March 56 NS.— April 25 NS. Then Sunday next after March 22 NS.=Maich 
27 NS. the date of NS. Easter. And Sunday next after April 25 NS.=May 1st 
NS. the date of the Greek Easter at 5 weeks after NS. Easter. (AC. Notes 89, 92, 
109-119 ; AM.) 

MDC 4th Example. Use this reference for 

MDT. Construction. For VGND. reverse MDT. 2d Ex., and from the standard 
AD. 1836 March 20.837,442 NS. Cal. find Jan. 118.548,378 Min. OS. in JP. 
Then solar dates recede in Julian time 0.007,784 day per year, for the difference 
between a Julian year of 335.25 days and a mean year of 365.242,216 days. Then : 

For FGND. before the equinox (to use them also for Mosaic dates), find YGND. 
=JP. 1 Jan. 118.540,594. Subtract a lunation of 29.530.589 leaving Jan. 89.010,- 
005 as in the table for the earliest limit. Then lunar dates recede 10.882,932 days in a 
common year as in the table, for the difference between 12 lunations and 385.25 
days, and advance 18.647,657 for 13 lunations in an embDlismic year. 

Then reverse MDT. 1st Ex., and from the standard FGND. = AD. 1853 Sept. 
17.993,023 NS. Cal. in GN. 11, find JP. 11 Jan. 92.803,814 Min. OS. as in the table, 
next after the solar date Jan. 89.010,005. Then JP. 11=GN. 11, is 10 years after 
GN. 1. And 10 X 10.882,932 -~ 29.539,539 leaves 20.237,553 recession from JP. 1 
to JP. 11, which add to 92.803,314 = Jan. 113.043,867 = FGND. of GN. 1 as in 
the table. Then for FGND. of successive years within the limits and next before 
the vernal equinox, continue to subtract 10.8S2,932, unless this leave less than 
89.010,005, and in that case add 18.647,657. Thus find all FGND. from JP. 1 to 
JP. 20, or from GN. 1 to the next GN. 1, and the second will be 0.031,585 day less 
than the first, because 325 lunations of 29.530,589 days, are 0.031,585 day less than 
19 years of 865.25 days, as in MDT. Rule 1. 

For lunar dates for all time the GN. and FGND. are alone required. But Mosaic 
dates are solar as well as lunar, and these are explained under MDT. Mosaic. 
'HC. Notes 57-67.) 

16 



APPENDIX. 





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17 



APPENDIX. 

MDE. Bute 1. Construction. By MDT. find the date of the vernal equinox AD. 
1831, Jan. Min. 67.220,682 OS. Stand. Then add 12 NS. SC, and subtract 59 fo* 
March min. 20.220,682 NS. Stand. Then continue to subtract 0.007,784 for the dif- 
ference between a Julian year of 365.25 and a mean year of 365.242,216. And this 
continued to AD. 1900=March 20.072,986. But Feb. 29 is omitted in AD. 1900, 
and makes NS. SC=13 days, so that in AD. 1900, VGND.=March 21.072,986 
min. 

Then, for FGND. : By MDT. find the date of full moon AD. 1881 = GN. 1, Jan. 
Min. 15.082,105 NS. Stand. Then as for MDT., continue to subtract 10.S82,932, 
unless this gives the date before Jan. 1st, and then add 18.647,657, which is the 
same as 10.882,932 subtracted to find the date of the twelfth moon, and then a lu- 
nation of 29.530,589 added to find the next later moon. Thus find all the moons 
which fall in January during the cjcie. And then to each continue to add luna- 
tions of 29.530,5S9 days to the end of the year in the day of Jan. And then by 
Jan. Min. table, translate Jan. Min. into Month min. 

'MDE. Bule2. To perpetuate MDE. Table. ForVGND., add 4713 to the year 
AD. for the year JP. Multiply the year JP. by 0.007,784 and subtract P from 
Jan. 118.548,37S for VGND. in terms of Jan. Min., OS., Stand. Then add NS. SC. 
and subtract 59 for the day of March Min., NS., Stand. 

Then for FGND. : Add one to the year AD. and divide S by the circle 19 for 
R=GN. Then find the difference between that year and the year in the table 
which has the same GN. Divide by 19 this difference of years, and multiply Q 
by 0.061,585, and add the product to all the FGND. in the table if the given year 
be before the date in the table, or subtract it if after that date, for all the dates in 
the new cycle from GN. 1 to GN. 19 — provided they be in the same century. And 
if not, then subtract 12 days and add NS. SC. for date NS. 

MDE. 1st Example. AD. 1853+1 ; -f-19=GN. 11, =38 years before AD. 1891. 
Then 33-19=2 ;X0.061, 585=0.123,172, which add to Sept. 17.620 in the table = 
Sept. 17.743 min. in JC. 1. Add 0.25 JCC.=Sept. 17.993, Cal. NS. And the 
standard FGND.=Sept. 17.993,023 (MD. Second). 

MDE. 2d Example. Compare the mean dates in the table +JCC.=0.25 with the 
actual dates (in parentheses) as given in ANA. in AD. 1881 =GN. 1, viz. : Jan. 
15.332(15.482); Feb. 13.863 (14.267); Mar. 15.393(15.942); April 13.924(14.403); 
May 13.454 (13.933); June 11.985 (12.290); July 11.516 (11.592); Aug. 10.046 
(9.880); Sept. 8.577 (8.194); Oct. 8.107 (7.583); Nov. 6.638 (6.085); Dec. 6.169 
(5.718). Hence the actual was 0.569 more than the mean in April, and 0.553 less 
than the mean in Nov. The extremes were 0.568,302 more and less in the standard 
cycle of variations (MD. Second). (AC. Table 1.) 

MDE. M Example. Compare the same with the medium dates of GN. 1 dis- 
tributed in the Egyptian cycle in AC. Table 1, and the days are the same except 
0.076 less in April and 0.015 in June. But this is unusually close for the Egyptian 
cycle, which counts nothing less than whole days, and makes no difference for the 
extra day in a leap year. 

MDT. Constructwn. (MDC. 4th Example.) 

18 



APPENDIX. 



MD r.=Mean Date by Table. In 
terms of JP., Jan. Min., OS., Stand. 
Rule 1. For FGND. Divide the given 
year JP. by the circle 19 for Q of past 
cycles and R=GN. Then multiply 
Q by 0.061,585, and subtract P from 
FGND. opposite to GN. as found, 
and R=FGND. in terms of Jan. 
Min., OS., Stand. Then reduce Jan. 
Min., OS., Stand. (MDC. 4th Ex.) 

MDT.EuleM. ForVGND. multi- 
ply the given year JP. by 0.007,784 
and subtract P from Jan. Min. 
118.548,078 and R=VGND. in terms 
of Jan. Min., OS., Stand. Then re- 
duce. 

MDT. 1st Ex, For FGND. in AD. 
1853; +4713= JP. 6586 ;-=-19=Q 345 
+ GN. 11. Then 345 X 0.061,585 
from FGND. 92.806,314 = FGND. 
Jan. Min. 71.559,489 OS. Add 12 
NS. SC. for date NS. and 0.25 JCC. 
for cal. and 177.183,534 for 6 luna- 
tions = Jan. Cal. 260. 993, 023= Sept. 
17.993,023 the standard mean date of 
full moon (MD. 1st Ex.). 

MDT. U Ex. For VGND. in AD. 1806. Then 1866 + 4713 = JP. 6579; 
X 0.007, 784 from 118. 548,378= Jan. Min. 07.337,442 OS. Add 12 NS. SC.= 
March Min. 20.337,442 NS. In JC. 2 add 0.50 JCC.=March 20.837,442 NS. Cal., 
the standard in MD. 3d Ex. 

MDT. Mosaic. Bide. If the given year be not before the year JP. of coinci- 
dence, and not as late as the year AD. of coincidence, find FGND. by the rule of 
MDT. in minimum standard time. Then add 0.098,148 for the local time at Jeru- 
salem, and 0.25 for Hebrew minimum time counted from 6 hours before midnight 
at Jerusalem, and the result will be the date of the Mosaic full moon of Nisan, on or 
within one lunation after the vernal equinox. But if the given year be before the 
year JP. of coincidence, then add to FGND. thus found a lunation of 29.530,589 
for the date of the Mosaic full moon of Nisan. And if the given year be on or 
after the year AD. of coincidence, then subtract a lunation from the date thus 
found. (HC. Notes 58-67 ; AC. Notes 82, 90.) 

MDT. M Ex. For FGND. Mosaic in AD. 1883 ; +4713=JP. 6596 ; -*-19=Q 
347+GN. 3. This is between JP. 6001 and AD. 7788, so that no correction is re- 
quired. Then by MDT. 347x0.061,585 from 91.278,003 = FGND. Jan. Min. 
69.908,008 OS. Stand. Add 12 NS. SC. and in Jan. Min. table find March Min. 
22.908,008. Then for JC. 3 add 0.75, and for Hebrew time add 0.348, 148= March 
24.003,153 Cal. Hebrew. (HC. Notes 20, 28-33.) 

Note. HC. Table shows AD. 1883=HC. GN. 1, and Moled Tisri Oct. 2. .0. .879. 

19 



JP. 


AD. 




89.010,005 


Year 


Year 




-10.882,933 
+18.647,657 


of 
Coinci. 


of 
Coinci. 


GN. 




FGND. 


1211 


2998 


1 


113.043,867 


3606 


5393 


2 


102.160,935 


6001 


7788 


3 


91.278,003 


1896 


3683 • 


4 


109.925,660 


4290 


6077 


5 


99.042,728 


185 


1972 


6 


117.690,385 


2580 


4367 


7 


106.807,453 


4974 


6761 


8 


95.924,521 


869 


2656 


9 


114.572,178 


3264 


5051 


10 


103.689,246 


5659 


7446 


11 


92.806,314 " 


1553 


3340 


12 


111.453,971 


3948 


5735 


13 


100.571,039 


6343 


8130 


14 


89.688,107 


2238 


4025 


15 


108.335,764 


4632 


6419 


16 


97.452,832 


527 


2314 


17 


116.100,489 


2922 


4709 


18 


105.217,557 


5317 


7104 


19 


94.334,625 


2dl 


112.982,282 






lstl 
JE. 


113.043,867 


-0.061,585 



APPENDIX. 

For full moon of Nisan subtract 1C2. .10. .42 leaves April £2. .14. 837. And Apri 
22 is the date of the passover. Then subtract one HC. lunation of 29. .12. .793 
leaves March 24 2 h. .44 scruples. This shows that in HC. GN. 1 the HC. full 
moon is the full moon of Zif. (HC. Notes 20, 28-33.) 

MDT. 4th Ex. For full moon of Nisan in maximum Hebrew time for consecutive 
years for AD. 1800 to AD. 1818 in AC. Note 89 : Find the date of the vernal equi- 
nox AD. 1807, Jan. 67.798,698 in minimum standard time OS. Then add 12.00 
NS. SC. for NS., and 0.75 JCC. for max., and 0.348,148 for Hebrew time, and 
subtract 59 for the day of March, make March 21.894,846 max. Hebrew the date 
of the vernal equinox in AD. 1807. Then make this the limit for the earliest date 
of the full moon of Nisan. 

Then find the date of full moon AD. 1807, March 24.252,496 in maximum He- 
brew time. Then, as in the construction of MDT. table, continue to subtract 
10.882,902 for next year, unless that make the date earlier than the equinox, and 
then add 18.647,657 (or the difference between a lunation of 29.530,559 and an 
epact of 10.882,932). This is in maximum time to agree with the Egyptian rules, 
so as to take the latest date upon which the moon can fall. (AC. Notes 89-91.) 

MDT. Qth Ex. For full moon of Nisan in calendar time, counted from 6 hours 
before midnight at Jerusalem from AD. 1883 to AD. 1903 : Find the minimum 
standard date OS. of the vernal equinox in AD. 1883, Jan. min. OS. 67.205,114. 
Then add 12 days NS. SC, and 0.348,148 for Hebrew time, and 0.75 JCC. for 
calendar time = maximum in JC. 3, and subtract 59 for the day of March. These 
make the date of the vernal equinox AD. 1883, March 21.303,270. Make this the 
limit. Then find the date of full moon, next after the equinox AD. 1883, March 
23.256,153 in minimum Hebrew time, and from this and subsequent dates subtract 
10.882.932 unless this give the moon before the equinox, and then add 18.647,057 
to find the date of the full moon of Nisan of the next year in minimum Hebrew 
time. Then for calendar or actual time counted from 6 hours before midnight at 
Jerusalem, add to these dates JCC. =0.00 in JC. ; 0.25 in JC. 1 ; 0.50 in JC. 2 ; 
0.75 in JC. 3. (AC. Notes 89.) 

These dates are in calendar, or ordinary time, to compare with dates by HC. and 
HCM., because those dates are in calendar time. And either of these dates can be 
found hy MDT. Mosaic. And the years of coincidence show that all the GN. in 
that table give the full moons of Nisan from AD. 1883 to AD. 1903, so that March 
21.666,160 min. in 1894 being the earliest, this might be made the limit instead of 
the equinox March 21.303,270. And for tabulating, the dates are first found in 
Julian years of 365.25 days, because uniform, and then by JCC. reduced to the 
irregular calendar time with 3 years of 865 days, and one year of 366 days. 

MDT. Mosaic, Explanation. 19 mean years of 365.242,216 days =6989. 602, 104. 
And 235 lunations of 29 530,589 days=6939.638,415. The difference 0.080,311 
divided by 19=0.004,542,08 day per year, that the 235th moon represented by any 
GN. advances in mean equinoxial date. And this divided into 29.580,589= 
6500,697 years that the moon represented by any GN. will advance a full lunation 
later than the vernal equinox and become the moon of Zif. And 65C0-r- 19=342.1 
years interval, at which the GN. iu succession reach the same equinoxial date, and 
in the reverse order of the GN. rule, or add 11 or subtract 8 years. 

Now : In MDT. table, the limit is one lunation before the vernal equinox in 
JP. 1. Hence all the FGND. are before YGND. from JP. 1 to JP. 19, and are 

20 



APPENDIX. 

the Mosaic full moons of Adar in terms of JP., Jan. min., OS., Stand., in the first 
JP. cycle. The latest=Jan. min. 117.690,385 of JP. 6. This will first reach 
VGND. and become the Mosaic full moon of Nisan. Then for VGND. in JP. 6 ; 
6X0.007,784 from 118.548,378=VGND. 118.501,674, subtract 117.690,385=0.811,- 
289 that FGND. was before VGND. This divided by 0.004,542,68 gives 179 years 
for FGND. of GN. 6 to reach VGND., so that JP. 6+179=JP. 185 the year of 
coincidence of GN. 6. Then to JP. 185 continue to add 342.1 for the successive 
years of coincidence, and for the corresponding GN. continue to add 11 in a circle 
of 19 to GN. 6, and record these years JP. of coincidence opposite to their respect- 
ive GN., as the years* in which the FGND. represented full moon on or next after 
VGND. Then add 6500 years for the years of coincidence of the next earlier 
moon in the same year and record this date in terms of AD. Hence : " JP. year 
of coincidence " gives the year in which the full moon of that GN. advances from 
Adar to Nisan, and becomes the moon of Nisan, and the "AD. year of coincidence " 
6500 years later, gives the year in which the same moon will advance to the month 
Zif , and the tull moon one lunation earlier will coincide with the vernal equinox 
and become the full moon of Nisan. This is in accordance with the Mosaic rule. 
But not according to the present Hebrew Calendar. (AC. Notes 6-11, 75-80.) 

MBT. mil Ex. In AD. 325 new moon fell March 31.321,421 in Hebrew time. 
(MDB. 8th Ex.) (AC. Note 101.) 

ME.= Mohammedan Era=Turkish Calendar. (C.) 

Mean dates and revolutions, are the meaus between the extreme variations of the 
actual more and less than the mean. To these mean dates corrections are applied 
to find the actual, according to the conditions which produce these variations. 
(MD. 1st, 3d Ex.) 

Meridian, is a great circle of the earth which passes through the poles, the zenith 
and the nadir, and is true North and South along the earth. The word signifies 
noon, and at apparent noon, the sun is on the meridian. (Prime, Greenwich.) 

Metonic Cycle (OE.). 

j/z'?i. =Minimum Julian time. (JCC, Jan. Min.) 

Missale Romanum=SQTvice Book of the Church of Rome, and contains NS. in 
the Roman form, while the Anglican Prayer Books contain NS. in the Anglican 
form, and more simple to reach the same result. (NS. Table 7. AC. Notes 
120-130.) 

Mohammedan i?ra=ME. (C.) 

Moled=Birih of the moon=new moon. Moled Tohn=Birth of the moon at the 
Creation =first Moled Tisri=mean conjunction in Hebrew time counted from 6 
hours before midnight at Jerusalem, and making 18 hours signify conjunction at 
noon of the date found by rule. 

Month, Gal. and Min. =day of the month, Cal. or min. 

Moon, new and full. (MD.) 

Mosaic fo'»z0=Hebrcw time. And Mosaic rule made it impossible for Nisan to 
begin before 18 hours after conjunction, or full moon to fall later than the end of 
the 14th Nisan. And the Mosaic full moon of Nisan, fell on or next after the ver- 
nal equinox. (AC. Notes 6-11, 75-80.) 

Movable Feasts, depend upon the date of Easter in NS.; OS.; AM. (C.) 

Nabonassar, Era of =NE. (C.) 

Madir—V\\imb downwards (Zenith). 

21 



APPENDIX. 

Nautical time is 12 hours less than Standard. 

_ZVt7.=Nicean Calendar. (AC. Note 1 ; JE. Table.) 

.ZV.£r.=Era of Nabonassar. (C.) 

New Moon- Moled, NGN., MD. 

NGND.=T$ew Moon GND. 

Nicean Calendar = NC 

Nisan= First Mosaic month. And 14th Nisan was the Mosaic date of the full 
moon, which fell on or next after the vernal equinox. 

Nodes=pomis where the moon crosses the equator and the ecliptic. (DAGND. ; 
DDGND.; LAGND.; LDGND.; Zero.) 

Nomikon Pascha, i. e., Passover by the Law=date of AM. GN., to represent the 
date of the full moon of Nisan. (AM., MDC.) 

Nones or Ninths, by Roman account, but as we count, 8 days before the Ides. 
(Ides, JE. Table.) 

NS. Introduction. NS.=New Style = Gregorian Calendar (C). All dates AD. 
were OS., until 10 days NS. SC. were added to Oct. 5, making Oct. 5-15 AD. 
1582 in Rome, Spain, Portugal ; Dec. 10-20 AD. 1582 in Brabant, Flanders, Hai- 
nault ; Dec. 15-25 AD. 1583 in France ; AD. 1585 in the Romish provinces of Ger- 
many ; AD. 1586 in Poland ; AD. 1587 in Hungary. Then 11 days Sept. 4-15 
AD. 1752 in England and colonies ; AD. 1778 in Prussia. The Russo-Greeks still 
retain OS. And this began with JE., Jan. 1 BC. 45. (Year.) 

NS. &t7.=NS. Solar Correction =12 days from March 1 AD. 1800 to March 1 
AD. 1900, and then 13 days from March 1 AD. 1900 to March 1 AD. 2100, etc. 
Rule : Subtract 12 from the centuries AD. Divide R by 4 for Q and 2d R. 
Multiply Q by 3 and to P add the 2d R and the constant 7 and S=NS. SC, which 
added to OS.=NS., and subtracted from NS.=OS. Thus for AD. 1800. 18-12 
= 6 ;-^4=Q 1+2 ; Q 1x3+2+7=12 NS. SC. (NS. Table II.) 

Nundinal Letters=K to H, repeated through a common year in the Julian Calen- 
dar, to indicate each " Ninth" day in Roman account, or each eighth day as we 
count. This was the origin of our Sunday Letters to indicate each seventh clay 
throughout the year. (JE. Table.) 

0^.=Olympic Era=01ympic Calendar. (C.) 

011= number of days after conjunction. 

Olympiads=OB. (C.) 

Oriental C7m?Y?7i=Russo-Greek Church=AM. (Westerns.) 

OS. =01d Style, as dates were counted before NS. Introduction. It counts all 
years AD., which leave no remainder when divided by 4, to be leap years. This 
includes AD. 1800, 1900, 2100, etc., which NS. counts as common years. The 
astronomical rules for all time MDB., MDT., are in OS., and each fourth year is 
counted a leap year, and this is carried back to the beginning of JP., on account 
of its uniformity. Then when required after NS. Introduction OS. is reduced to 
NS. by adding NS. SC. But the Russo-Greeks still retain OS., and in correspond- 
ence with Westerns both dates are given, as April 1-13, 1885. (JE., MDC.) 

OS. FGNJD. (MDB.) 

PA=Practical Astronomy. (Zero.) 

Pascha. (Hgion, Nomikon, AM.; MDC, AC. Notes 108-119.) 

Paschal Canons. These were the solar portions of the first Christian Calendar 
(NO, and fixed the date of Easter on Sunday next after the full moon of Nisan. 

22 



APPENDIX. 

which fell on or next after the 21st day of March. And March 21 was the maxi- 
mum Julian date of the vernal equinox in AD. 325, or the actual date in each 
third year after leap year, while it fell on March 20 in AD. 325. This might make 
Easter fall later than the date determined by the Council of Nicea, but it prevented 
Easter falling on the 14th Nisan (th,e anniversary of Crucifixion), as the main object 
of the Council. (AC. Notes 1-11.) 

Paschal Limits^ March 21 and April 18. (AC. Notes 66-70.) 

Passover, falls on the 15th Nisan. By the Mosaic rule the 15th Nisan was the 
day after full moon. By the present rules, the 15th Nisan is the day of full moon, 
and GN. HC. 1, 9, 12 make it the full moon of Zif. (AC. Notes 6-11, 75-80, 89.) 

Pengee=VG'N'D. =moon nearest to the earth. (AGND.) 

PG7iV#.=PerigeeGND. (Zero.) 

Poles of the earth = points in the heavens around which the stars appear to 
revolve. And equidistant from the equator. Poles of the heavens are equidistant 
from the ecliptic. 

Precession of the equinoxes. (Equinox ; AC. Notes 99, 101, 129, 130 ; NE. Notes 
19-35.) 

Pref. =Pref ace to the Calendars. 

Precise. The astronomical rules (MD.) are in precise accordance with a mean 
year of 365.242,216 days, and a mean lunation of 29.530,589 days. (MD. First 
and Second.) 

Prime meridian= standard of longitude and time. In 1874 the delegates from 
many nations met at Washington, D. C, and all except the French, agreed to 
make Greenwich, Eng., the universal prime meridian, and to count time from 
midnight at Greenwich. Previously GNA., and the nautical part of ANA. counted 
in Nautical time from noon at Greenwich. This was used by all English-speaking 
navigators, who were said to be 70 per cent, of the whole. (Stand.) 

The prime meridian of the Hebrew Calendar in ancient times was Jerusalem, 
since the date depended on the appearance of new moon at Jerusalem. The pres- 
ent Hebrew Calendar gives the date of the new moon on the basis of Jerusalem as 
the prime meridian. All Christian calendars (NC, OS., AM. NS.) have been 
framed to give the correct date of Easter. And Easter is a Hebrew date. So that 
Jerusalem is the prime meridian of all Hebrew and Christian calendars. It would 
be a better prime meridian for longitude and time than is Greenwich. But the 
change would cause large expenses for new charts, and might at first produce 
confusion. 

M= Remainder. 

Recession, per cycle=JE. if marked minus= ~- (MDC, MDT.). Also of the 
vernal equinox=0.007,784 day per year in terms of OS. for the difference between 
a Julian year of 365.25 days, and a mean year of 365.242,216 days. Also of the 
moon represented by any GN. in terms of OS. =0.003,241,316 day per year, for 
the difference between the recession of the equinox 0.007,784 day per year, and the 
advance of the moon in equinoxial date 0.004, 542, 684, 2 day per year. (AC. Notes 
31, 36.) 

Retraction JST8., of all GN. which fall on April 19, and of all from GN. 12 to 19 
which fall on April 18, to keep them within the Paschal limits, March 21 and 
^pril 18. (AC. Notes 66-70.) 

Bight Ascension =AR. 

23 



APPENDIX. 

Roman Calendars =AU. ; JE. And the Romans counted both extremes, making 
one more than we count, as shown by the dates in JE. Table and Nundinal letters. 
And as the French now call a week = Eight days, and two weeks = Fifteen days. 

Russo-Greek Church=AM. (C.) 

Sign (Equinox ; Zodiac). 

Solar Correction=NS. SC. and AC. SC. (AC. Notes 31, 41-46.) Also in HCM. 
to keep the full moon of Nisan, on or the next after the vernal equinox. 

Solar Cycle. Rule : Find the year of the solar cycle from the year JP. in the 
rule for Chronological Cycles. And opposite to that year find the Dominical OS. 
in the Solar Cycle OS., and the Dominical NS. in the Solar Cycle NS., as follows * 

Solar Cycle OS. — for ever. 



lg,F 


5b 


A 


9 d, C 


13 f, E 


17 a 


G 


21 c 


B 


25 e 


D 


2 E 


6 


G 


10 B 


14 D 


18 


F 


22 


A 


26 


C 


3 D 


7 


F 


11 A 


15 C 


19 


E 


23 


G 


27 


B 


4 C 


8 


E 


12 G 


16 B 


20 


D 


24 


F 


28 


A 



Solar Cycle NS.— March 1, 1800, to March 1, 1900. 



1 e 


D 


5 g 


F 


9 b 


A 


13 d 


C 


17 f 


E 


21 a 


G 


25 c 


B 


2 


C 


6 


E 


10 


G 


14 


B 


18 


D 


22 


F 


26 


A 


3 


B 


7 


D 


11 


F 


15 


A 


19 


C 


23 


E 


27 


G 


4 


A 


8 


C 


12 


E 


16 


G 


20 


B 


24 


D 


28 


F 



For any other century, add one day to NS„ SC, and divide S by the circle 7, 
and R 1 to 7— A to G=Dominical for year 28 of the cycle. Then as above, write 
down the letters A to G and repeat, doubling the letters at the leap years, and the 
small letters are for dates before Feb. 29, in the years of the cycle 25, 21, 17, 13, 9, 
5, 1. Or find the same by the memorized rule for the Dominical. 

Solar Cycle of AM., is not as convenient as Solar Cycle OS., and gives the same 
result. (AM.) 

And the Solar Cycle NS. can be used for OS. dates after adding NS. SC. to find 
the corresponding date NS. And vice versa. (MDC. 3d Ex.) 

Solstice. Summer Solstice is when the sun is at the Tropic of Cancer, and 
furthest North, at Declination 23° 27' North of the Equator. The Winter Solstice 
is when the sun is at the Tropic of Capricorn, and furthest South, at Declination 
23° 27' South of the Equator. The average time of the four cardinal points in the 
year are 20, 21, 23, 22 of March, June, September, December. (Equinox.) 

Stand. = Standard time counted from midnight at Greenwich. (Local, Nautical, 
Civil, Prime.) 

Sunday Letters. Memorized (AC. Note 71 ; JE. Table). 

Synodic revolution of the moon, from full to full, or from new to new=a mean 
lunation of 29.530,589 days. 

Syzygy=new and full moon=sun, moon, and earth "joined together." 

Thoth— Beginning of the Egyptian year (AE.; NE.). 

24 



APPENDIX. 

Transit— sun, moon, or star on the meridian. 

Tropic (Solstice). 

Tropical ymr=mean year of 365,242,216 days. 

Turkish Calendar (ME.). 

Variations of actual from mean. (MD. 1st, 2d Ex.) 

Vernal equinox=YGN. (Equinox, MDB., MDC., MDT.). 

VOJSf.— Vernal equinox=Zero of solar date*. 

Visible new moon determines the beginning of the Turkish year, as it did the b&. 
ginning of the Mosaic year. But at present the Hebrew year begins before con 
junction (ME., AC. Notes 6-11, 75, 76). 

Wandering year— Canicular year of the Egyptians contained 12 months of 80 
days and 5 epagomenai=365 days. It therefore receded in Julian time one day in 
four years, and hence was called the Wandering year (NE.> AE. HC. Notes 139- 
156). 

Westerns =those who use GN. JP. in the form of GN. OS. or GN. NS., as dis~ 
tinguished from the Orientals, who use GN. AM. (AC. Notes ; AM., OS.). 

Year. A mean or equinoxial year=365. 242,216 days. A Julian year=365.25 
days. A lunar year =854 days or 12 lunations alternately 30 and 29 days. The 
Hebrew years have 353, 354, 355, 883, 384, 385 days (HC). 

Tear Beginning and adoption of NS. The year began in England and Ireland 
on Dec. 25, until changed to Jan. 1, 1067 ; then to March 25, in 1155, for the legal 
and ecclesiastical year, but Jan. 1 was considered the beginning of the Julian year. 
Then the " supputation " from March 25 (Annunciation day) shall be changed to 
Jan. 1, 1752, and Sept. 3 be called Sept. 14, 1752 (CP. of 1607 and Bond Pref. 19). 
The year began in Scotland on March 25 until Jan. 1, 1600. In France on Dec. 
25, and Easter eve, and March 25 until Jan. 1, 1564, and NS. was adopted Dec. 
11-21, 1582. In Rheims on March 25 from 12th century ; in Diocese of Soissons, 
Dec. 25 in 13th century. In Amiens on Easter eve in 13th century. In Picardy 
on Jan. 1, after 18th century. In Languedoc and many other southern provinces 
on March 25 before 12th century, and on Easter eve in 12th and 13th centuries. In 
Toulouse on Easter eve until 1564. In Narbonne and Pays do Foix on Dec. 25 
until 1564. Diocese of Limoges on Easter and March 25 in 1301. In Poitou, Nor- 
mandy, and Anjou on Dec. 25, when they fell into the hands of the English. In 
Dauphiny on March 25 towards the end of the 18th century, then Dec. 25 in the 
L4th century, and called <c Le Style Delphinal." In Province from Dec. 25 to Jan. 
1., and March 25 and Easter in 11th, 12th, 18th cent. Besancon on March 25 before 
15th cent , then Jan. 1 in 15th cent. , and settled by edicts in 1574, 1575, 1576. Mont- 
billiard on Jan. 1 and March 25 before 1564. In Germany on Dec. 25, until Jan. 1, 
1544 (and NS. adopted by Roman Catholics Dec. 22— Jan. 1, 1583, and by Prot- 
estants 19 Feb.— 1 March, 1700). In Cologne on Easter before 1310, then Dec. 25 
in 1310. In Cologne University, March 25 until 1428 ; in Mentz or Mayence, Dec. 
25 until 15th cent., then Jan. 1. In Prussia on Dec. 25 until Jan. 1, 1559 (and NS. 
in 1583). In Roman Catholic Netherlands Jan. 1, 1556 (and NS. adopted in Flan- 
ders, Brabant, Artois, and Hainault Dec. 25, 1582=Jan. 1, 1583). In Protestant 
Netherlands = Holland, Zealand, Friesland, Groningen, Overyssel, Utrecht, Guild- 
eriand, Zitphen on Jan. 1, 1586 (and NS. Feb. 19=March 1, 1700). In Lorraine on 
Dec. 25, and on March 25, and on Easter before Jan. 1, 1579 (and NS. Dec. 10-20, 
1582). In Rome, Milan, and a great part of Italy, on Dec. 25 in the 13th, 14th, 15th 

25 



APPENDIX. 

centuries, until Jan. 1, 1582 (and NS. on Oct. 5-15, 1582). In Tuscany on March 
25 from 10th century to Jan. 1, 1751, known as the "Era of Florence." In Venice 
on March 1 for the legal year before 1522, then Jan. 1, 1522, for civil and legal 
year. In Savoy on Easter before Jan. 1, 1635 (and NS., Dec. 22= Jan. 1, 1583, and 
NS. in Hungary, 1587). In Sweden on Jan. 1, 1559 (and NS. on March 1-12, 
1753). In Denmark on Dec. 25 or Aug. 12, until Jan. 1, 1559 (and NS. on Feb. 
19— March 1, 1700). In Lausanne and Pays de Vaud on March 25, until in the 
Grisons, Jan. 1, 1717, and Swiss Cantons, Jan. 1, 1739 (and NS. by Roman Catholics 
D CC> 22— Jan. 1, 1583, and by Protestants Jan. 1-12, 1701). In Spain on Jan. 1, 
1556 (and NS. on Oct. 5-15, 1582). In Arragon on March 25 until Dec. 25, 1350, 
then Jan. 1, 1556. In Castile on March 25 until Dec. 25, 1383, then Jan. 1, 1556. 
In Portugal on March 25, then Dec. 25, 1420, then Jan. 1, 1556 (and NS. on Oct. 
5-15, 1582). In Russia in the spring in 11th century, then Greek Calendar, then 
Jan. 1, 1725 (NS. has not been adopted by Russia and Greece). In Poland on Jan. 
1, 1626. In France Sept. 22, 1792 and Jan. 1, 1806, and leap year, called the 
"Olympic year" (Bond, pp. 17-28 ; Jarvis, pp. 95-97). 

Zero = The point in a revolution that is used as the standard from which to 
measure other points. And half zero = half a revolution. In PA. these terms are 
used for FGN, NGN., AGN., PGN., DAGN., DDGN., LAGN., LDGN. But 
for calendars the first three only are required (MDB., MDC, MDE., MDT.). 

Zodiac. The sun in its annual round passes through twelve constellations of the 
fixed stars, and most of these being supposed to represent animals, these constella- 
tions are called the zodiac, from the Greek word Zoon, an animal. And 30 degrees 
along the ecliptic is assigned to each, and is called a Sign of the Zodiac. The 
point where the sun strikes the equator at the vernal equinox is called "the First 
point of Aries." Then counting eastward, the signs and constellations follow in 
this order : The Ram, Bull, Twins, Crab, Lion, Virgin, Scales, Scorpion, Archer, 
Goat, Waterman, Fishes. These can be remembered by the following distich in 
Latin : 

Sunt Aries, Taurus, Gemini, Cancer, Leo, Virgo, 
Libraque, Scorpius, Arcitenens, Caper, Amphora, Pisces. 

But the "Precession of the equinoxes" has carried the astronomers' "First point 
of Aries " westward among the stars about one sign of the zodiac, or 30 degrees, so 
that Hamal (the brightest star of Aries, and near its western border) culminates 
two hours after the astronomers' first point of Aries. And in like manner all the 
other constellations are about two hours later than the astronomers' Signs of the 
Zodiac of the same name. 

These astronomical facts are involved in the examination of ancient calendars. 
But they would be unknown if there were no fixed stars. They have no effect 
upon the seasons. These depend exclusively upon the revolution of the earth 
around the sun, without regard to the fixed stars. Jarvis and Seabury are two of 
the three who are known to attribute to the Precession of the equinoxes the reces- 
sion of dates that was caused by the difference between the artificial Julian year of 
365.25 days and the equinoxial year of 365.242,216 days (AC. Notes 99, 101 ; 12ft 
130). 



26 






ATJTHOKS.* 



Ada, or Adda, Rabbi, born in Babylon AD. 188. HC. 8, 14, 17, 136. 

Adams, Roman Antiquities. AC. 15, 131, 132 ; AU. 2, 3, 6 ; JE. 12, 17 ; NC. 3 

Contra.; NS. (p. 14). 
Adler, Chief Rabbi of Great Britain. HC. (p. 11), 87-89, 135, 155. 
Agapius Tontsarenko ("Father Agapius "). AM. 13-19 ; AC. 112. 
Alphonsi Tabulae Astronomical, Paris, Ann. 1545. AC. 131, 132. 
AM.=Modera Greek Calendar. AC. 108-119, 126, 127 ; HC. 120 ; NS. (pp. 3, 14, 

15); Scale, 7 ; Indiction (A.); MDC. 3 Ex. (A.). 
ANA. = American Nautical Almanac. ME. 3 Ex., 4, 25 ; OE. (p. 1), 65, 66. 
Anglican Rules. AC. 2, 21, 30, 106, 109-112, 124-130 ; GND. 8 ; NC. 3 ; NS. 

(p. 3). 
Anthon's Classical Dictionary. AC. 78 ; JE. 7, 17. 
Archbishop of Corinth. AC. 74, 95, 108-119. 
Aries, Council of. AC. 3. 
Astor Library. AC. 132 ; AM. 15 ; HC. (p. 11). 
Barnard, F. A. P. Pp. 538-589, Journal Gen. Con. Prot. Epis, Church in 1871. 

AC. 132 ; NS. (p. 14). 
Blunt's Annotated Book of Common Prayer. AC. 80 bis ; 1&2. 
Bond's Days and Years (A.). 
Brady's Clavis Calandria. AC. 3, 12, 54, 80 bis, 96, 101, 105, 131, 132; AM. 3; 

HC. (p. 11), 11 ; JE. 8, 17 ; NC. 6 ; NS. (pp. 14, 15). 
Calippus. OE. Preface, 13, 22, 30-32. 
Calmet's Dictionary of the Bible. HC. (p. 11). 

Censorinus wrote AD. 238. AE. 1 Ex., 4 Ex., 2 ; HC. Ill ; NE. 6 Ex., 13 ; OE. 2. 
Chalcedon, Council of. AC. Summary, 88, 106 ; AM. 2 ; GND. 12 ; HC. 131 ; 

NS. (p. 15). 
Churchman's Calendar of 1866-7-8. AC. 109-119. 
Connaisance des Temps. AC. 35 ; ME. 3 Ex., 4, 25. 
Crelle, Journal die Mathematik. HC. (p. 11), 7, 11, 122. 
Crucifixion. Preface ; AC. Summary, 3, 4, 8, 107, 123 ; HCM. (p. 8) ; HC. 78-83, 

114, 164-179 ; NC. 5. 
Cruden's Concordance. HC. (p. 12), 11, 151. 
Delambre, Histoire de l'Astronomie Moderne. AC. 12, 30, 34, 78, 96, 97, 101, 131, 

132 ; ME. 2 ; NC. 6 ; NS. (pp. 3, 14). 
De Morgan, Book of Almanacs, and Rules of NS. in GNA. of 1846. AC. 73, 132. 
Diodorus Siculus. OE. 47-54. 



* A figure standing alone = number of the note, as HC. 8 ; and with p. = page, as HC. (p. 11), 
and with Ex. = Example, as MDC. 3 Ex. ; (A.), i. «., in Appendix. 

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nmm^I 0F CONGRESS 



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